منابع مشابه
Vertex-transitive CIS graphs
A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and vertex-transitive if, for every pair of vertices, there exists an automorphism of the graph mapping one to the other. We show that a vertex-transitive graph is CIS if and o...
متن کاملCores of Vertex Transitive Graphs
A core of a graph X is a vertex minimal subgraph to which X admits a homomorphism. Hahn and Tardif have shown that for vertex transitive graphs, the size of the core must divide the size of the graph. This motivates the following question: when can the vertex set of a vertex transitive graph be partitioned into sets each of which induce a copy of its core? We show that normal Cayley graphs and ...
متن کاملLimits of vertex-transitive graphs
The class of all connected vertex-transitive graphs with finite valency forms a metric space under a natural combinatorially defined metric. We prove some basic properties of this metric space and discuss the structure of graphs which are limit points of the subset consisting of all finite graphs that admit a vertex-primitive group of automorphisms. A description of these limit graphs would pro...
متن کاملCompression of Vertex Transitive Graphs
We consider the lossless compression of vertex transitive graphs. An undirected graph G = (V, E) is called vertex transitive if for every pair of vertices x, y ∈ V , there is an automorphism σ of G, such that σ(x) = y. A result due to Sabidussi, guarantees that for every vertex transitive graph G there exists a graph mG (m is a positive integer) which is a Cayley graph. We propose as the compre...
متن کاملSelf-Complementary Vertex-Transitive Graphs
A graph Γ is self-complementary if its complement is isomorphic to the graph itself. An isomorphism that maps Γ to its complement Γ is called a complementing isomorphism. The majority of this dissertation is intended to present my research results on the study of self-complementary vertex-transitive graphs. I will provide an introductory mini-course for the backgrounds, and then discuss four pr...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1983
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(83)80007-9