On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Baghipur, Maryam, Ghorbani, Modjtaba, Ganie, Hilal A. and Shang, Yilun (2021) On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue. Mathematics, 9 (5). p. 512. ISSN 2227-7390

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Official URL: https://doi.org/10.3390/math9050512


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.

Item Type: Article
Additional Information: Funding information: This research was funded by Northumbria Univeristy under grant number 201920A1001.
Uncontrolled Keywords: signless Laplacian reciprocal distance matrix (spectrum); spectral radius; total reciprocal distance vertex; Harary matrix
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Elena Carlaw
Date Deposited: 02 Mar 2021 12:37
Last Modified: 01 Sep 2021 13:31
URI: http://nrl.northumbria.ac.uk/id/eprint/45581

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