Upper and Lower Bounds for the Spectral Radius of Generalized Reciprocal Distance Matrix of a Graph

Yuzheng Ma, Yubin Gao and Yanling Shao
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Yuzheng Ma: School of Data Science and Technology, North University of China, Taiyuan 030051, China
Yubin Gao: School of Mathematical Sciences, North University of China, Taiyuan 030051, China
Yanling Shao: School of Mathematical Sciences, North University of China, Taiyuan 030051, China

Mathematics, 2022, vol. 10, issue 15, 1-12

Abstract: For a connected graph G on n vertices, recall that the reciprocal distance signless Laplacian matrix of G is defined to be R Q ( G ) = R T ( G ) + R D ( G ) , where R D ( G ) is the reciprocal distance matrix, R T ( G ) = d i a g ( R T 1 , R T 2 , ⋯ , R T n ) and R T i is the reciprocal distance degree of vertex v i . In 2022, generalized reciprocal distance matrix, which is defined by R D α ( G ) = α R T ( G ) + ( 1 − α ) R D ( G ) , α ∈ [ 0 , 1 ] , was introduced. In this paper, we give some bounds on the spectral radius of R D α ( G ) and characterize its extremal graph. In addition, we also give the generalized reciprocal distance spectral radius of line graph L ( G ) .

Keywords: graph; generalized reciprocal distance matrix; reciprocal distance signless Laplacian matrix; spectral radius (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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