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

Abstract

For a connected graph G on n vertices, recall that the reciprocal distance signless Laplacian matrix of G is defined to be RQ(G)=RT(G)+RD(G), where RD(G) is the reciprocal distance matrix, RT(G)=diag(RT1,RT2,⋯,RTn) and RTi is the reciprocal distance degree of vertex vi. In 2022, generalized reciprocal distance matrix, which is defined by RDα(G)=αRT(G)+(1−α)RD(G),α∈[0,1], was introduced. In this paper, we give some bounds on the spectral radius of RDα(G) and characterize its extremal graph. In addition, we also give the generalized reciprocal distance spectral radius of line graph L(G).