On the Sum and Spread of Reciprocal Distance Laplacian Eigenvalues of Graphs in Terms of Harary Index

The reciprocal distance Laplacian matrix of a connected graph G is defined as RDL(G)=RT(G)−RD(G), where RT(G) the diagonal degrees and RD(G) Harary matrix. Clearly, RDL(G) real symmetric matrix, we denote its eigenvalues λ1(RDL(G))≥λ2(RDL(G))≥…≥λn(RDL(G)). largest eigenvalue λ1(RDL(G)) RDL(G), denoted by λ(G), called spectral radius. In this paper, obtain several upper bounds for sum k in terms various parameters, such order n, maximum degree RTmax, minimum RTmin, index H(G) G. We determine extremal cases corresponding to these bounds. As consequence, radius λ(G) parameters mentioned above characterize cases. Moreover, attain lower spread RDLS(G)=λ1(RDL(G))−λn−1(RDL(G)) parameters. graphs many