ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS

Year 2026, Volume: 16 Issue: 4 , 521 - 535 , 07.04.2026

Surya S Pramada Ramachandran

https://izlik.org/JA56WH77AS

Abstract

The eccentricity matrix of a graph $ G $ is derived from its distance matrix by letting the $ ij ^{th}$ entry be equal to the distance between two vertices $ i $ and $ j $, if the distance is the minimum of their eccentricities and zero otherwise. The eigenvalues of the eccentricity matrix of $ G $ are called $ \varepsilon $-eigenvalues. Its $ \varepsilon $-spectrum is the set of $ \varepsilon $-eigenvalues together with its multiplicity and $ \varepsilon $-energy is the sum of the absolute values of the $ \varepsilon $-eigenvalues. In this paper, we study the $ \varepsilon $-spectra of certain operations on regular graphs. We also established some bounds on $ \varepsilon $-energy of graphs and characterize the extreme graphs.

Keywords

eccentricity matrix , distance matrix , spectrum , energy , eigenvalue

Thanks

The authors would like to express their sincere gratitude to the anonymous referees for their valuable comments and insightful feedback, which have greatly improved the quality and clarity of this work.

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