Interconnections between the different energies of the complements of regular graphs

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, Karnatak University’s Karnatak Arts/Science College Dharwad 580001, Karnataka, India

2 Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Gorukle Campus-16059, Bursa, Turkey

Abstract

The energy of a graph G is determined by the absolute sum of its eigenvalues. Similar to this concept, the distance energy, Harary Energy, Seidel energy, complementary distance energy and reciprocal complementary distance energy are all defined based on the eigenvalues of their respective matrices. In this paper, we study these energies on the complement of a regular graph G in terms of the energy of G. We explore exact relationships among these energies. Recent studies have explored equienergetic graphs concerning the adjacency and distance matrices. In this paper, we provide graphs illustrating the equienergetic properties with respect to six matrices. The results obtained extend some of the existing findings.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 14 August 2025

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