On Q-spectral integral variation

Kirkland, Steve (2009) On Q-spectral integral variation. Electronic Notes in Discrete Mathematics, 35. pp. 203-208. ISSN 1571-0653

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Let G be a graph with two non adjacent vertices and G0 the graph constructed from G by adding an edge between them. It is known that the trace of Q0 is 2 plus the trace of Q, where Q and Q0 are the signless Laplacian matrices of G and G0 respectively. So, the sum of the Q0-eigenvalues of G0 is the sum of the the Q- eigenvalues of G plus two. It is said that Q-spectral integral variation occurs when either only one Q-eigenvalue is increased by two or two Q-eigenvalues are increased by 1 each one. In this article we present some conditions for the occurrence of Q-spectral integral variation under the addition of an edge to a graph G.

Item Type: Article
Keywords: signless Laplacian matrix; Q-integral graph; Q-spectral integral variation;
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 2192
Depositing User: Professor Steve Kirkland
Date Deposited: 14 Oct 2010 14:49
Journal or Publication Title: Electronic Notes in Discrete Mathematics
Publisher: Elsevier
Refereed: Yes

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