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dc.contributor.authorLee, Guang-Siangen_US
dc.contributor.authorWeng, Chih-wenen_US
dc.date.accessioned2014-12-08T15:23:25Z-
dc.date.available2014-12-08T15:23:25Z-
dc.date.issued2012-10-01en_US
dc.identifier.issn0097-3165en_US
dc.identifier.urihttp://hdl.handle.net/11536/16403-
dc.description.abstractThe 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 2d + 1 must be distance-regular, generalizing a recent result of van Dam and Haemers. (C) 2012 Elsevier Inc. All rights reserved.en_US
dc.language.isoen_USen_US
dc.subjectDistance-regular graphsen_US
dc.subjectEigenvaluesen_US
dc.subjectSpectral excess theoremen_US
dc.titleA spectral excess theorem for nonregular graphsen_US
dc.typeArticleen_US
dc.identifier.journalJOURNAL OF COMBINATORIAL THEORY SERIES Aen_US
dc.citation.volume119en_US
dc.citation.issue7en_US
dc.citation.epage1427en_US
dc.contributor.department應用數學系zh_TW
dc.contributor.departmentDepartment of Applied Mathematicsen_US
dc.identifier.wosnumberWOS:000305820200004-
dc.citation.woscount5-
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