The signature of k-cyclic graphs of ∞-type

Let be a simple graph with vertex set and edge set . The signature of is the difference between the number of positive eigenvalues and the number of negative eigenvalues of the adjacency matrix . In [22, Linear Algebra Appl. 2013;438:331-341], it was conjectured that , where denotes the number of cy...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 64; no. 3; pp. 375 - 382
Main Authors Wang, Dengyin, Tian, Fenglei
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.03.2016
Taylor & Francis Ltd
Subjects
Graphs
Linear algebra
nullity
positive inertia index
signature of a graph
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Summary:Let be a simple graph with vertex set and edge set . The signature of is the difference between the number of positive eigenvalues and the number of negative eigenvalues of the adjacency matrix . In [22, Linear Algebra Appl. 2013;438:331-341], it was conjectured that , where denotes the number of cycles in of length , and denotes the number of cycles in of length . The authors of this paper have established the conjecture for trees, unicyclic graphs and bicyclic graphs. We prove the conjecture for -cyclic graphs of -type, that is, the graphs in which and in which no two cycles have a common vertex.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2015.1041708