Bounds on eigenvalues and chromatic numbers

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作者
Cao, DS
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O29 [应用数学];
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070104 ;
摘要
We give new bounds on eigenvalue of graphs which imply some known bounds. In particular, if T(G) is the maximum sum of degrees of vertices adjacent to a vertex in a graph G, the largest eigenvalue rho(G) of G satisfies rho(G) less than or equal to root T(G) with equality if and only if either G is regular or G is bipartite and such that all vertices in the same part have the same degree. Consequently, we prove that the chromatic number of G is at most root T(G) + 1 with equality if and only if G is an odd cycle or a complete graph, which implies Brook's theorem. A generalization of this result is also given. (C) 1998 Elsevier Science Inc.
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页码:1 / 13
页数:13
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