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.
متن کاملMaximum degree in graphs of diameter 2
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 ....
متن کاملOn Diameter of Line Graphs
The diameter of a connected graph $G$, denoted by $diam(G)$, is the maximum distance between any pair of vertices of $G$. Let $L(G)$ be the line graph of $G$. We establish necessary and sufficient conditions under which for a given integer $k geq 2$, $diam(L(G)) leq k$.
متن کاملThe maximum genus of graphs of diameter two
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, ...
متن کاملMaximum pebbling number of graphs of diameter three
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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90047-j