On diameter and distance energy of complement of regular graphs

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Karnatak University's Karnatak Arts/Science College, Dharwad, Karnataka, India.

2 Department of Mathematics, Karnatak University Dharwad, Karnataka, India.

Abstract

In this paper, we investigate the diameter and distance energy of the complement of a regular graph $G$. We improve and extend earlier results on the diameter and distance energy of graph complements obtained by Indulal [Algebr. Struct. Appl. 4 (2017) 53-58], removing the restrictions on the relationship between the degree $r$ and the order $n$ of the graph. We also derive a formula for the distance energy of the complement of a regular graph in terms of its adjacency energy and eigenvalues. This formula facilitates the characterization and construction of families of distance equienergetic graphs from adjacency equienergetic ones. Furthermore, we enhance some findings related to an open problem concerning adjacency and distance equienergetic graphs.

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References

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Algebraic Structures and Their Applications

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Available Online from 28 August 2025

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