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 $SLEE(G)=\sum^{n}_{i=1}e^{q^{}_i}$‎, ‎where $q^{}_1‎, ‎q^{}_2‎, ‎\dots‎, ‎q^{}_n$ 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.

Keywords

Main Subjects


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