The maximum genus of vertex-transitive graphs
نویسندگان
چکیده
منابع مشابه
The maximum genus of vertex-transitive graphs
Graphs possessing a high degree of symmetry have often been considered in topological graph theory. For instance, a number of constructions of genus embeddings by means of current or voltage graphs is based on the observation that a graph can be represented as a Cayley graph for some group. Another kind of embedding problems where symmetrical graphs are encountered is connected with regular map...
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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 ...
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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...
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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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1989
ISSN: 0012-365X
DOI: 10.1016/0012-365x(89)90175-1