Graphs which are locally a cube

AbstractWe prove that there are exactly two connected graphs which are locally a cube: a graph on 15 vertices which is the complement of the (3×5)-grid and a graph on 24 vertices which is the 1-skeleton of a certain 4-dimensional regular polytope called the 24-cell

A revised Moore bound for mixed graphs

The degree-diameter problem seeks to find the maximum possible order of a graph with a given (maximum) degree and diameter. It is known that graphs attaining the maximum possible value (the Moore bound) are extremely rare, but much activity is focused on finding new examples of graphs or families of graph with orders approaching the bound as closely as possible. There has been recent interest in this problem as it applies to mixed graphs, in which we allow some of the edges to be undirected and some directed. A 2008 paper of Nguyen and Miller derived an upper bound on the possible number of vertices of such graphs. We show that for diameters larger than three, this bound can be reduced and we present a corrected Moore bound for mixed graphs, valid for all diameters and for all combinations of undirected and directed degrees

Locally Pkn graphs

We completely classify the graphs all of whose neighbourhoods of vertices are isomorphic to Pkn (2 ≤ k < n), where Pkn is the k-th power of the path Pn of length n - 1.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Maximal cubic graphs with diameter 4

We prove that there is no cubic graph with diameter 4 on 40 vertices. This implies that the maximal number of vertices of a (3,4)-graph is 38. © 2000 Elsevier Science B.V.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Locally Cn k graphs

We completely classify the graphs all of whose neighbourhoods of vertices are isomorphic to Cn k (2 ≤ k < n), where Cn k is the k-th power of the cycle Cn of length n. © 1995, Belgian Mathematical Society.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Orbits on vertices and edges of finite graphs

Given two integers ν > 0 and ε{lunate} >/ 0, we prove that there exists a finite graph (resp. a finite connected graph) whose automorphism group has exactly ν orbits on the sets of vertices and ε{lunate} orbits on the set of edges if and only if ν ≤ 2ε{lunate} + 1 (resp. ν ≤ ε{lunate} + 1). © 1985.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Quelques conditions locales et extrêmales en théorie des graphes

Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe