Extremal Values for the Maximum Degree in a Twin-Free Graph

Ars Combinatoria, Vol. 107, pp. 257-274, 2012.

Irène CHARON, Olivier HUDRY & Antoine LOBSTEIN
Centre National de la Recherche Scientifique
Ecole Nationale Supérieure des Télécommunications
46 rue Barrault, 75634 Paris cédex 13, France
{irene.charon, olivier.hudry, antoine.lobstein}@telecom-paristech.fr

Abstract. Consider a connected undirected graph G=(V,E) and an integer r greater than or equal to 1; for any vertex v in V, let B_r(v) denote the ball of radius r centred at v, i.e., the set of all vertices linked to v by a path of at most r edges. If for all vertices v in V, the sets B_r(v) are different, then we say that G is r-twin-free.
In r-twin-free graphs, we prolong the study of the extremal values that can be reached by some classical parameters in graph theory, and investigate here the maximum degree.

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