On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Maryam Baghipur*, Modjtaba Ghorbani, Hilal Ahmad Ganie, Yilun Shang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.
Original languageEnglish
Article number512
Number of pages12
JournalMathematics
Volume9
Issue number5
DOIs
Publication statusPublished - 2 Mar 2021

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