[1] |
O. Favaron, A. Hansberg, and L. Volkmann.
k-domination and minimum degree in graphs.
J. Graph Theory, 57 no 1:33-40, 2008.[ bib ] A subset |

[2] |
O. Favaron, H. Karami, and S.M. Sheikholeslami.
Total domination in K_{5}- and K_{6}-covered graphs.
Discrete Math. Theor. Comput. Science, 10:1:35-42, 2008.[ bib ] A graph |

[3] |
O. Favaron and M. A. Henning.
Total domination in claw-free graphs with minimum degree two.
Discrete Math., 308 (15):3213-3219, 2008.[ bib ] A set |

[4] |
O. Favaron and M. A. Henning.
Bounds on total domination in claw-free cubic graphs.
Discrete Math., 308 (16):3491-3507, 2008.[ bib ] A set |

[5] |
O. Favaron, H. Karami, and S.M. Sheikholeslami.
Total domination and total domination subdivision numbers of a graph
and its complement.
Discrete Math., 38 (17):4018-4023, 2008.[ bib ] A set |

[6] |
M. Chellali, O. Favaron, T. W. Haynes, and D. Raber.
Ratios of some domination parameters in trees.
Discrete Math., 308 (17):3879-3887, 2008.[ bib ] |

[7] |
M. Blidia, M. Chellali, O. Favaron, and N. Meddah.
Maximal k-independent sets in graphs.
Discuss. Math. Graph Theory, 28:151-163, 2008.[ bib ] |

[8] |
M. Blidia, M. Chellali, and O. Favaron.
Ratios of some domination parameters in graphs and claw-free graphs.
In J. A. Bondy et al., editors, Graph Theory in Paris, pages
61-72. Trends Math., Birkhauser, Basel, 2007.[ bib ] In the class of all graphs and the class of claw-free graphs, we give exact bounds on all the ratios of two graph parameters among the domination number, the total domination number, the paired domination number, the double domination number and the independence number. We summarize the old and new results in a table and give for each bound examples of extremal families. |

[9] |
M. Blidia, M. Chellali, O. Favaron, and N. Meddah.
On k-independence in graphs with emphasis on trees.
Discrete Math., 307 no 17-18:2209-2216, 2007.[ bib ] In a graph |

[10] |
O. Favaron, H. Karami, and S.M. Sheikholeslami.
Total domination and total domination subdivision numbers.
Austral. J. Combin., 38:229-235, 2007.[ bib ] A set |

[11] |
O. Favaron, R.C. Laskar, and D. Rautenbach.
t-partitions and s-complete t-partitions of a graph.
Austral. J. Combin., 36:295-302, 2006.[ bib ] A partition { |

[12] |
O. Favaron.
An alternative definition of the k-irredundance.
AKCE J. Graphs Comb., 2(1):33-38, 2005.[ bib ] In accordance with the k-domination and the k-independence introduced by Fink and Jacobson in 1985, Jacobson, Peters and Rall defined in 1990 the concept of |

[13] |
O. Favaron.
Bounds on total and paired domination in graphs and claw-free graphs.
pages 59-73, 2005. [ bib ] We survey the knowns results concerning upper bounds on the parameters of domination, total domination and paired domination of a graph in terms of its order and minimum degree. These bounds are established in the class of all graphs and in the class of claw-free graphs. For two of them concerning total and paired domination in claw-free graphs, we give more details and an idea of the proofs. |

[14] |
M. Blidia, M. Chellali, and O. Favaron.
Independence and 2-domination in trees.
Austral. J. Combin., 33:317-327, 2005.[ bib ] In a graph a vertex is said to dominate all its neighbours. A 2-dominating set of a graph |

[15] |
E. J. Cockayne, O. Favaron, and C. M. Mynhardt.
On i^{-}-Edge-Removal-critical graphs.
Discrete Math., 276(1-3):111-125, 2004.[ bib ] We are interested in the behaviour of the independent domination number |

[16] |
E. J. Cockayne, O. Favaron, and C. M. Mynhardt.
Total domination in K_{r}-covered graphs.
Ars Combin., 71:289-303, 2004.[ bib ] A graph |

[17] |
O. Favaron, G. Fricke, W. Goddard, S. M. Hedetniemi, S. T. Hedetniemi,
P. Kristiansen, R. C. Laskar, and D. Skaggs.
Offensive alliances in graphs.
Discuss. Math. Graph Theory, 24:263-275, 2004.[ bib ] A set |

[18] |
O. Favaron, T. W. Haynes, and S. T. Hedetniemi.
Domination subdivision in graphs.
Utilitas Math., 66:195-209, 2004.[ bib ] A set |

[19] |
O. Favaron and M. A. Henning.
Paired domination in claw-free cubic graphs.
Graphs Combin., 20(4):447-456, 2004.[ bib ] A set |

[20] |
O. Favaron, G. H. Fricke, D. Pritikin, and J. Puech.
Irredundance and domination in kings graphs.
Discrete Math., 262(1-3):131-147, 2003.[ bib ] Each king on an |

[21] |
O. Favaron, M. Mahéo, and J.-F. Saclé.
The Randic index and other Graffiti parameters of graphs.
MATCH - Commun. Math. Comput. Chem., 47:7-23, 2003.[ bib ] Many graph parameters are of interest for both chemists and mathematicians, especially when they are related to the degrees, the distances, or the eigenvalues of the adjacency matrix of the graph. Fajtlowicz developed a program called Graffiti which proposes conjectures obtained by comparing such parameters. We prove or disprove some of these conjectures and give a short survey on general results concerning one of them, the Randic index. |

[22] |
E. J. Cockayne, O. Favaron, W. Goddard, P. J. Grobler, and C. M. Mynhardt.
Changing upper irredundance by edge addition.
Discrete Math., 266(1-3):185-193, 2003.[ bib ] Denote the upper irredundance number of a graph |

[23] |
O. Favaron and M. A. Henning.
Upper total domination in claw-free graphs.
J. Graph Theory, 44(2):148-158, 2003.[ bib ] A set |

[24] |
C. Delorme, O. Favaron, and D. Rautenbach.
Closed formulas for the numbers of small independent sets and
matchings and an extremal problem for trees.
Discrete Appl. Math., 130:503-512, 2003.[ bib ] We derive closed formulas for the numbers of independent sets of size at most 4 and matchings of size at most 3 in graphs without small cycles that depend only on the degree sequence and the products of the degrees of adjacent vertices. As a related problem we describe an algorithm that determines a tree of given degree sequence that maximizes the sum of the products of the degrees of adjacent vertices. |

[25] |
O. Favaron.
Independence and upper irredundance in claw-free graphs.
Discrete Appl. Math., 132(1-3):85-95, 2003.[ bib ] It is known that the independence number of a connected claw-free graph |

[26] |
E. J. Cockayne, O. Favaron, and C. M. Mynhardt.
Secure domination, weak roman domination and forbidden subgraphs.
Bull. Inst. Combin. Appl., 39:87-100, 2003.[ bib ] Bounds are obtained for the secure domination number γ |

[27] |
O. Favaron, S. T. Hedetniemi, S. M. Hedetniemi, and D. F. Rall.
On k-dependent domination.
Discrete Math., 249(1-3):83-94, 2002.[ bib ] A subset |

[28] |
O. Favaron, T. W. Haynes, S. T. Hedetniemi, M. A. Henning, and D. J. Knisley.
Total irredundance in graphs.
Discrete Math., 256(1-2):115-127, 2002.[ bib ] A set |

[29] |
C. Delorme, O. Favaron, and D. Rautenbach.
On the Randic index.
Discrete Math., 257(1):29-38, 2002.[ bib ] The Randic index |

[30] |
G. Bacsó and O. Favaron.
Independence, irredundance, degrees and chromatic number in graphs.
Discrete Math., 259(1-3):257-262, 2002.[ bib ] Let β ( |

[31] |
C. Delorme, O. Favaron, and D. Rautenbach.
On the reconstruction of the degree sequence.
Discrete Math., 259(1-3):293-300, 2002.[ bib ] The edge reconstruction conjecture due to Harary says that all graphs |

[32] |
E. J. Cockayne, O. Favaron, and C. M. Mynhardt.
Total domination in claw-free cubic graphs.
J. Combin. Math. Combin. Comput., 43:219-225, 2002.[ bib ] We prove that the total domination number of an n-vertex claw-free cubic graph is at most n/2. |

[33] |
E. J. Cockayne, O. Favaron, P. J. Grobler, C. M. Mynhardt, and J. Puech.
Ramsey properties of generalised irredundant sets in graphs.
Discrete Math., 231 (1-3):123-134, 2001.[ bib ] For each vertex |

[34] |
O. Favaron, M. A. Henning, J. Puech, and D. Rautenbach.
On domination and annihilation in graphs with claw-free blocks.
Discrete Math., 231 (1-3):143-151, 2001.[ bib ] Let γ( |

[35] |
O. Favaron.
Inflated graphs with equal independence number and upper irredundance
number.
Discrete Math., 236 (1-3):81-94, 2001.[ bib ] The inflation |

[36] |
O. Favaron, E. Flandrin, H. Li, and Z. Ryjácek.
Clique covering and degree conditions for hamiltonicity in claw-free
graphs.
Discrete Math., 236 (1-3):65-80, 2001.[ bib ] By using the closure concept introduced by the last author, we prove that for any sufficiently large nonhamiltonian claw-free graph |

[37] |
E. J. Cockayne, O. Favaron, P. J. Grobler, C. M. Mynhardt, and J. Puech.
Generalised Ramsey numbers with respect to classes of graphs.
Ars Combin., 59:279-288, 2001.[ bib ] Let H |

[38] |
O. Favaron and P. Fraisse.
Hamiltonicity and minimum degree in 3-connected claw-free graphs.
J. Combin. Theory Ser. B, 82 (2):297-305, 2001.[ bib ] Using Ryjácek's closure, we prove that any 3-connected claw-free graph of order |

[39] |
O. Favaron and Y. Redouane.
Neighborhood unions and regularity in graphs.
Theoretical Computer Science, 263:247-254, 2001.[ bib ] One way to generalize the concept of degree in a graph is to consider the neighborhood |

[40] |
E. J. Cockayne, O. Favaron, and C. M. Mynhardt.
Irredundance-edge-removal-critical graphs.
Utilitas Math., 60:219-228, 2001.[ bib ] We characterise the graphs |

[41] |
O. Favaron.
Extendability and factor-criticality.
Discrete Math., 213 (1-3):115-122, 2000.[ bib ] |

[42] |
S. Brandt, O. Favaron, and Z. Ryjácek.
Closure and stable hamiltonian properties in claw-free graphs.
J. Graph Theory, 34 (1):30-41, 2000.[ bib ] In the class of |

[43] |
O. Favaron, M. A. Henning, C. M. Mynhardt, and J. Puech.
Total domination in graphs with minimum degree three.
J. Graph Theory, 34 (1):9-19, 2000.[ bib ] |

[44] |
O. Favaron, T. W. Haynes, and P. J. Slater.
Distance-k independent domination sequences.
J. Combin. Math. Combin. Comput., 33:225-237, 2000.[ bib ] |

[45] |
E. J. Cockayne, O. Favaron, C. M. Mynhardt, and J. Puech.
A characterisation of (γ -i)-trees.
J. Graph Theory, 34 (4):277-292, 2000.[ bib ] |

[46] |
O. Favaron.
From irredundance to annihilation: a brief overview of some
domination parameters of graphs.
Saber (Venezuela), 32 (2):64-69, 2000.[ bib ] |

[47] |
J. Brousek, O. Favaron, and Z. Ryjácek.
Forbidden subgraphs, hamiltonicity and closure in claw-free graphs.
Discrete Math., 196(1-3):29-50, 1999.[ bib ] We study the stability of some classes of graphs defined in terms of forbidden subgraphs under the closure operation introduced by the second author. Using these results, we prove that every 2-connected claw-free and |

[48] |
O. Favaron and J. Puech.
Irredundant and perfect neighborhood sets in graphs and claw-free
graphs.
Discrete Math., 197-198 (1-3):269-284, 1999.[ bib ] |

[49] |
O. Favaron, E. Flandrin, H. Li, and F. Tian.
An Ore-type condition for pancyclability.
Discrete Math., 206 (1-3):139-144, 1999.[ bib ] |

[50] |
R. J. Faudree, O. Favaron, E. Flandrin, H. Li, and Z. Liu.
On 2-factors in claw-free graphs.
Discrete Math., 206 (1-3):131-137, 1999.[ bib ] |

[51] |
M. Cai, O. Favaron, and H. Li.
(2,k)-factor-critical graphs and toughness.
Graphs Combin., 15:137-142, 1999.[ bib ] |

[52] |
C. Delorme and O. Favaron.
Graphs with a small max-cut.
Util. Math., 56:153-165, 1999.[ bib ] |

[53] |
O. Favaron, V. Kabanov, and J. Puech.
The ratio of three domination parameters in some classes of claw-free
graphs.
J. Combin. Math. Combin. Comput., 31:151-159, 1999.[ bib ] |

[54] |
M. Shi, X. Yuan, M. Cai, and O. Favaron.
(3,k)-factor-critical graphs and toughness.
Graphs Combin., 15:463-471, 1999.[ bib ] |

[55] |
O. Favaron and J. Puech.
Irredundance in grids.
Discrete Math., 179:257-265, 1998.[ bib ] |

[56] |
A. Ainouche, O. Favaron, and H. Li.
Global insertion and hamiltonicity in DCT-graphs.
Discrete Math., 184:1-13, 1998.[ bib ] |

[57] |
R. J. Faudree, O. Favaron, and H. Li.
Independence, domination, irredundance, and forbidden pairs.
J. Combin. Math. Combin. Comput., 26:193-212, 1998.[ bib ] |

[58] |
O. Favaron.
Irredundance in inflated graphs.
J. Graph Theory, 28(2):97-104, 1998.[ bib ] |

[59] |
E. J. Cockayne, O. Favaron, C. M. Mynhardt, and J. Puech.
An inequality chain of domination parameters for trees.
Discussiones Mathematicae-Graph Theory, 18:127-142, 1998.[ bib ] |

[60] |
O. Favaron and M. Shi.
Minimally k-factor-critical graphs.
Austral. J. Combin., 17:89-97, 1998.[ bib ] |

[61] |
E. J. Cockayne, O. Favaron, C. M. Mynhardt, and J. Puech.
Packing, perfect neighbourhood, irredundant and R-annihilated
sets in graphs.
Austral. J. Combin., 18:253-262, 1998.[ bib ] |

[62] |
O. Favaron, H. Li, and M. D. Plummer.
Some results on K_{r}-covered graphs.
Utilitas Math., 54:33-44, 1998.[ bib ] |

[63] |
O. Favaron and C. M. Mynhardt.
On equality in an upper bound for domination parameters of graphs.
J. Graph Theory, 24 (3):221-231, 1997.[ bib ] |

[64] |
O. Favaron and Y. Redouane.
Minimum independent generalized t-degree and independence number in
K_{1,r+1}-free graphs.
Discrete Math., 165/166:253-261, 1997.[ bib ] The minimum independent generalized t-degree of a graph |

[65] |
O. Favaron, F. Tian, and L. Zhang.
Independence and hamiltonicity in 3-domination-critical graphs.
J. Graph Theory, 25 (3):173-184, 1997.[ bib ] |

[66] |
O. Favaron, E. Flandrin, and Z. Ryjácek.
Factor-criticality and matching extension in DCT-graphs.
Discussiones Mathematicae-Graph Theory, 17:271-278, 1997.[ bib ] |

[67] |
O. Favaron, E. Flandrin, H. Li, Y. Liu, F. Tian, and Z. Wu.
Sequences, claws and cyclability of graphs.
J. Graph Theory, 21, no 4:357-369, 1996.[ bib ] |

[68] |
O. Favaron.
Least domination in a graph.
Discrete Math., 150:115-122, 1996.[ bib ] |

[69] |
O. Favaron, E. Flandrin, H. Li, and Z. Ryjácek.
Shortest walks in almost claw-free graphs.
Ars Combin., 42:223-232, 1996.[ bib ] |

[70] |
O. Favaron.
On k - factor-critical graphs.
Discussiones Mathematicae-Graph Theory, 16:41-51, 1996.[ bib ] |

[71] |
O. Favaron.
Signed domination in regular graphs.
Discrete Math., 158:287-293, 1996.[ bib ] |

[72] |
O. Favaron, H. Li, and R. H. Schelp.
Strong edge colorings of graphs.
Discrete Math., 159:103-109, 1996.[ bib ] |

[73] |
E. J. Cockayne, O. Favaron, and C. M. Mynhardt.
Universal maximal packing functions of graphs.
Discrete Math., 159:57-68, 1996.[ bib ] |

[74] |
O. Favaron and C. M. Mynhardt.
On the sizes of least common multiples of several pairs of graphs.
Ars Combin., 43:181-190, 1996.[ bib ] |

[75] |
R. J. Faudree, O. Favaron, E. Flandrin, and H. Li.
Pancyclism and small cycles in graphs.
Discussiones Mathematicae-Graph Theory, 16:27-40, 1996.[ bib ] |

[76] |
O. Favaron and M. Shi.
k-factor-critical graphs and induced subgraphs.
Congr. Numer., 122:59-66, 1996.[ bib ] |

[77] |
D. Amar, O. Favaron, P. Mago, and O. Ordaz.
Biclosure and bistability in a balanced bipartite graph.
J. Graph Theory, 20, no 4:513-529, 1995.[ bib ] |

[78] |
O. Favaron and J.-L. Fouquet.
On m-centers in P_{t}-free graphs.
Discrete Math., 125:147-152, 1994.[ bib ] |

[79] |
O. Favaron, D. P. Sumner, and E. Wojcicka.
The diameter of domination k-critical graphs.
J. Graph Theory, 18, no 7:723-734, 1994.[ bib ] |

[80] |
O. Favaron, M. Mahéo, and J.-F. Saclé.
Some eigenvalue properties in graphs (conjectures of Graffiti -
II).
Discrete Math., 111:197-220, 1993.[ bib ] |

[81] |
O. Favaron, P. Mago, C. Maulino, and O. Ordaz.
Hamiltonian properties of bipartite graphs and digraphs with
bipartite independence 2.
SIAM J. Discrete Math., 6, no 2:189-196, 1993.[ bib ] |

[82] |
R. J. Faudree, O. Favaron, E. Flandrin, and H. Li.
The complete closure of a graph.
J. Graph Theory, 17, no 4:481-494, 1993.[ bib ] |

[83] |
O. Favaron, P. Mago, and O. Ordaz.
On the bipartite independence number of a balanced bipartite graph.
Discrete Math., 121:55-63, 1993.[ bib ] |

[84] |
O. Favaron.
A note on the irredundance number after vertex-deletion.
Discrete Math., 121:51-54, 1993.[ bib ] |

[85] |
C. Delorme, O. Favaron, and M. Mahéo.
Isomorphisms of Cayley multigraphs of degree 4 on finite abelian
groups.
European J. Combin., 13:59-61, 1992.[ bib ] |

[86] |
O. Favaron.
A bound on the independence domination number of a tree.
International Journal of Graph Theory, 1, No 1:19-27, 1992.[ bib ] |

[87] |
E. J. Cockayne, O. Favaron, H. Li, and G. MacGillivray.
The product of the independent domination numbers of a graph and its
complement.
Discrete Math., 90:313-317, 1991.[ bib ] |

[88] |
O. Favaron, M.-C. Heydemann, J.-C. Meyer, and D. Sotteau.
A parameter linked with g-factors and the binding number.
Discrete Math., 91:311-316, 1991.[ bib ] |

[89] |
O. Favaron, M. Mahéo, and J.-F. Saclé.
On the residue of a graph.
J. Graph Theory, 15:39-64, 1991.[ bib ] |

[90] |
O. Favaron and D. Kratsch.
Ratios of domination parameters.
In Advances in Graph Theory, pages 173-182. V. Kulli, Vishwa
International Publications, 1991.[ bib ] |

[91] |
O. Favaron, M. Mahéo, and J.-F. Saclé.
Some results on conjectures of Graffiti - I.
Ars Combin., 29 C:90-106, 1990.[ bib ] |

[92] |
J.-C. Bermond, O. Favaron, and M. Mahéo.
Hamiltonian decomposition of Cayley graphs of degree 4.
J. Combin. Theory Ser. B, 46 (2):142-153, 1989.[ bib ] |

[93] |
O. Favaron and B. Hartnell.
On well-k-covered graphs.
J. Combin. Math. Combin. Comput., 6:199-205, 1989.[ bib ] |

[94] |
O. Favaron, M. Kouider, and M. Mahéo.
Edge-vulnerability and mean distance.
Networks, 19 (5):493-504, 1989.[ bib ] |

[95] |
O. Favaron.
Two relations between the parameters of independence and irredundance
in a graph.
Discrete Math., 70:17-20, 1988.[ bib ] |

[96] |
O. Favaron.
A note on the open irredundance in a graph.
Congr. Numer., 66:316-318, 1988.[ bib ] |

[97] |
O. Favaron.
k-domination and k-independence in graphs.
Ars Combin., 25 C:159-167, 1988.[ bib ] |

[98] |
O. Favaron and M. Kouider.
Path partitions and cycle partitions of eulerian graphs of maximum
degree 4.
Studia Sci. Math. Hungarica, 23:237-244, 1988.[ bib ] |

[99] |
O. Favaron.
Stabilité, domination, irredondance et autres paramètres de
graphes.
Thèse d'Etat, Université Paris-Sud, Orsay, France, 1986.[ bib ] |

[100] |
O. Favaron.
Equimatchable factor-critical graphs.
J. Graph Theory, 10 (4):439-448, 1986.[ bib ] |

[101] |
O. Favaron.
Stability, domination and irredundance in a graph.
J. Graph Theory, 10 (4):429-438, 1986.[ bib ] |

[102] |
O. Favaron and O. Ordaz.
A sufficient condition for oriented graphs to be hamiltonian.
Discrete Math., 58:243-252, 1986.[ bib ] |

[103] |
O. Favaron.
On a conjecture of Fink and Jacobson concerning k-domination and
k-dependence.
J. Combin. Theory Ser. B, 39 (1):101-102, 1985.[ bib ] |

[104] |
O. Favaron, Z. Lonc, and M. Truszczynski.
Decompositions of graphs into graphs with three edges.
Ars Combin., 20:125-146, 1985.[ bib ] |

[105] |
J. Ayel and O. Favaron.
Helms are graceful.
In Progress in Graph Theory, Proceedings Waterloo 1982, pages
89-92. A. Bondy and U. Murty, Academic Press Canada, 1984.[ bib ] |

[106] |
O. Favaron.
Very well covered graphs.
Discrete Math., 42:177-187, 1982.[ bib ] |

[107] |
E. J. Cockayne, O. Favaron, C. Payan, and A. G. Thomason.
Contributions to the theory of domination, independence, and
irredundance in graphs.
Discrete Math., 33:249-258, 1981.[ bib ] |

[108] |
O. Favaron, H. Karami, and S.M. Sheikholeslami.
Connected domination subdivision numbers of graphs.
Utilitas Math., To appear.[ bib ] A set |

[109] |
M. Chellali and O. Favaron.
On k-star-forming sets in graphs.
J. Combin. Math. Combin. Comput., To appear.[ bib ] Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs which extends only partially the well-known inequality chain γ( |

[110] |
O. Favaron, H. Karami, and S.M. Sheikholeslami.
Paired-domination number of a graph and its complement.
Discrete Math., to appear.[ bib ] |

[111] |
H. Aram, S.M. Sheikholeslami, and O. Favaron.
Trees with domination subdivision number three.
Discrete Math., to appear.[ bib ] A set |

[112] |
M. Chellali, O. Favaron, A. Hansberg, and L. Volkmann.
On the p-domination, the total domination and the connected
domination numbers of graphs.
J. Combin. Math. Combin. Comput., to appear.[ bib ] Fink and Jacobson [?] showed in 1985 that if |

[113] |
E. J. Cockayne, O. Favaron, A. Finbow, and C. M. Mynhardt.
Open irredundance and maximum degree in graphs.
Discrete Math., to appear.[ bib ] A necessary and sufficient condition for an open irredundant set of vertices of a graph to be maximal is obtained. This result is used to show that the minimum cardinality amongst the open irredundant sets in an |

[114] |
M. Blidia, O. Favaron, and R. Lounes.
Locating-domination, 2-domination and independence in trees.
Australasian J. Combin., to appear.[ bib ] |

[115] |
O. Favaron, H. Karami, and S.M. Sheikholeslami.
Disproof of a conjecture on the subdivision domination number of a
graph.
Graphs and Combinatorics, to appear.[ bib ] A set |

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