Reciprocal distance signless Laplacian spread of connected graphs

Yuzheng Ma (), Yubin Gao () and Yanling Shao ()
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Yuzheng Ma: North University of China
Yubin Gao: North University of China
Yanling Shao: North University of China

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 400-411

Abstract: Abstract Let G be a connected graph with vertex set $$V(G)=\{v_1,v_2,\ldots ,v_n\}$$ V ( G ) = { v 1 , v 2 , … , v n } . Recall that the reciprocal distance signless Laplacian matrix of G is defined to be $$RQ(G)=RT(G)+RD(G)$$ R Q ( G ) = R T ( G ) + R D ( G ) , where RD(G) is the reciprocal distance matrix, and $$RT_{i}$$ R T i is the reciprocal distance degree of vertex $$v_{i}$$ v i for $$i=1,2,\ldots ,n$$ i = 1 , 2 , … , n , $$RT(G)=\hbox {diag}(RT_{1},RT_{2},\ldots ,RT_{n})$$ R T ( G ) = diag ( R T 1 , R T 2 , … , R T n ) . Denote by $$\mu _{1}(RQ(G))$$ μ 1 ( R Q ( G ) ) and $$\mu _{n}(RQ(G))$$ μ n ( R Q ( G ) ) the largest eigenvalue and the least eigenvalue of RQ(G), respectively. The reciprocal distance signless Laplacian spread of G is defined as $$S_{RQ}(G)=\mu _{1}(RQ(G))-\mu _{n}(RQ(G))$$ S RQ ( G ) = μ 1 ( R Q ( G ) ) - μ n ( R Q ( G ) ) . In this paper, we obtain some bounds on reciprocal distance signless Laplacian spread of a graph.

Keywords: Graph; Reciprocal distance matrix; Reciprocal Distance signless Laplacian matrix; Reciprocal distance signless Laplacian spread; 05C50; 05C12; 15A18 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00373-7

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