The Signless Laplacian Estrada Index of Unicyclic Graphs

‎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 t...

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Veröffentlicht in:Mathematics interdisciplinary research (Online) 2017-12, Vol.2 (2), p.155-167
Hauptverfasser: Hamid Reza Ellahi, Ramin Nasiri, Gholam Hossein Fath-Tabar, Ahmad Gholami
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Sprache:eng
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Zusammenfassung:‎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.
ISSN:2476-4965
DOI:10.22052/mir.2017.57775.1038