On the reciprocal distance Laplacian spectral radius of graphs

Articles in Press

Document Type : Original paper

Authors

Department of Mathematics, University of Kashmir, Srinagar, India

Abstract

The reciprocal distance Laplacian matrix of a connected graph G is defined as RDL(G)=RTr(G)−RD(G), where RTr(G) is the diagonal matrix whose i-th element RTr(vi)=∑i≠j∈V(G)1dij and RD(G) is the Harary matrix. RDL(G) is a real symmetric matrix and we denote its eigenvalues as λ1(RDL(G))≥λ2(RDL(G))≥⋯≥λn(RDL(G)). The largest eigenvalue λ1(RDL(G)) of RDL(G) is called the reciprocal distance Laplacian spectral radius. In this paper, we obtain upper bounds for the reciprocal distance Laplacian spectral radius. We characterize the extremal graphs attaining this bound.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 11 July 2024

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