The Signless Laplacian Estrada Index of Unicyclic Graphs

Document Type : Special Issue: Energy of Graphs

Authors

1 Department of Mathematics, Faculty of Science, University of Qom, Qom, I R Iran

2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kahsan, Kashan, Iran

Abstract

‎For a simple graph G‎, ‎the signless Laplacian Estrada index is defined as SLEE(G)=∑ni=1eqi‎, ‎where q1‎, ‎q2‎,...‎, ‎qn are the eigenvalues of the signless Laplacian matrix of G‎. ‎In this paper‎, ‎we first characterize the unicyclic graphs with the first two largest and smallest SLEE's and then determine the unique unicyclic graph with maximum SLEE among all ‎unicyclic graphs on n vertices with a given diameter‎. ‎All extremal graphs‎, ‎which have been introduced in our results are also extremal with respect to the signless Laplacian ‎resolvent energy‎.

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Main Subjects

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Mathematics Interdisciplinary Research
Volume 2, Issue 2
December 2017
Pages 155-167

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