The superconnectivity of large digraphs and graphs
Proceedings of the first Malta conference on Graphs and combinatorics
Subsets with small sums in Abelian groups' I: the Vosper property
European Journal of Combinatorics
Connectivity of vertex and edge transitive graphs
Discrete Applied Mathematics
Graph Theory With Applications
Graph Theory With Applications
Super-Connectivity and Hyper-Connectivity of Vertex Transitive Bipartite Graphs
Graphs and Combinatorics
On the connectivity of diamond-free graphs
Discrete Applied Mathematics
Note: Super-connected edge transitive graphs
Discrete Applied Mathematics
Superconnected and Hyperconnected Small Degree Transitive Graphs
Graphs and Combinatorics
| Hi-index | 0.04 |
Let G be a graph of order n(G), minimum degree @d(G) and connectivity @k(G). We call the graph Gmaximally connected when @k(G)=@d(G). The graph G is said to be superconnected if every minimum vertex cut isolates a vertex. For an integer p=1, we define a p-diamond as the graph with p+2 vertices, where two adjacent vertices have exactly p common neighbors, and the graph contains no further edges. Usually, the 1-diamond is triangle and the 2-diamond is diamond. We call a graph p-diamond-free if it contains no p-diamond as a (not necessarily induced) subgraph. A graph is vertex transitive if its automorphism group acts transitively on its vertex set. In this paper, we give some sufficient conditions for vertex transitive graphs to be maximally connected. In addition, superconnected p-diamond-free (1@?p@?3) vertex transitive graphs are characterized.