The maximum genus of graphs with diameter three
نویسندگان
چکیده
منابع مشابه
The maximum genus of diameter three graphs
The maximum gen'us of connected of orient able surface on which G has 2-ce11 C:U.UYC;UUULl.".. to 2,M(G) where (3(G) the Betti n'umber of G.
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Skoviera, M., The maximum genus of graphs of diameter two, Discrete Mathematics 87 (1991) 175-180. Let G be a (finite) graph of diameter two. We prove that if G is loopless then it is upper embeddable, i.e. the maximum genus y,&G) equals [fi(G)/Z], where /3(G) = IF(G)1 IV(G)1 + 1 is the Betti number of G. For graphs with loops we show that [p(G)/21 2s yM(G) c &G)/Z] if G is vertex 2-connected, ...
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Given a configuration of pebbles on the vertices of a graph G, a pebbling move consists of taking two pebbles off some vertex v and putting one of them back on a vertex adjacent to v. A graph is called pebbleable if for each vertex v there is a sequence of pebbling moves that would place at least one pebble on v. The pebbling number of a graph G is the smallest integer m such that G is pebbleab...
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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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The purpose of this paper is to prove that, with the exception of C 4 , there are no graphs of diameter 2 and maximum degree d with d 2 vertices . On one hand our paper is an extension of [4] where it was proved that there are at most four Moore graphs of diameter 2 (i .e . graphs of diameter 2, maximum degree d, and d2 + 1 vertices) . We also use the eigenvalue method developed in that paper ....
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1999
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00037-5