Reciprocal distance Laplacian spectral radius of graphs

Articles in Press

Document Type : Original paper

Authors

1 Department of School Education JK Govt. Kashmir, India

2 Department of Mathematics, Smarkand International University of Technology, Samarkand 140100, Uzbekistan

3 Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK

Abstract

For a simple connected graph G with V(G)={v1,v2,…,vn}, let dij be the distance between any pair of distinct vertices vj and vj. The reciprocal distance Laplacian matrix RDL(G) of G is defined by RDL(G)=RTr(G)−RD(G), where RTr(G) is the diagonal matrix having i-the entry RTr(vi)=∑j∈V(G)1dij and RD(G) is the reciprocal distance matrix (also called Harary matrix) having (i,j)-th entry 1dij if i≠j and zero, otherwise. The set of all RDL(G)-eigenvalues δ1≥δ2≥⋯≥δn−1>δn is known as the RDL-spectrum (also called reciprocal distance Laplacian spectrum) of G and δ1 is called the RDL-spectral radius (also called reciprocal distance Laplacian spectral radius) of G. We explore various interesting properties of RDL-eigenvalues along with the bounds for RDL-spectral radius. We characterize the corresponding extremal graphs attaining these bounds.

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References

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Communications in Combinatorics and Optimization

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Available Online from 26 March 2025

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