A spectral excess theorem for nonregular graphs

Guang Siang Lee*, Chih-wen Weng


研究成果: Article同行評審

13 引文 斯高帕斯(Scopus)


The spectral excess theorem asserts that the average excess is, at most, the spectral excess in a regular graph, and equality holds if and only if the graph is distance-regular. An example demonstrates that this theorem cannot directly apply to nonregular graphs. This paper defines average weighted excess and generalized spectral excess as generalizations of average excess and spectral excess, respectively, in nonregular graphs, and proves that for any graph the average weighted excess is at most the generalized spectral excess. Aside from distance-regular graphs, additional graphs obtain the new equality. We show that a graph is distance-regular if and only if the new equality holds and the diameter D equals the spectral diameter d. For application, we demonstrate that a graph with odd-girth 2. d+. 1 must be distance-regular, generalizing a recent result of van Dam and Haemers.

頁(從 - 到)1427-1431
期刊Journal of Combinatorial Theory. Series A
出版狀態Published - 1 10月 2012


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