jaem TWMS Journal of Applied and Engineering Mathematics 2146-1147 2587-1013 Işık University Press Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics) Kombinatorik ve Ayrık Matematik (Fiziksel Kombinatorik Hariç) ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS https://orcid.org/0009-0003-7976-4299 S Surya St. Paul’s College, Kalamassery https://orcid.org/0000-0001-8647-0000 Ramachandran Pramada St. Paul’s College, Kalamassery 04 07 2026 16 4 521 535 03 13 2025 06 23 2025 Copyright © 2010, TWMS Journal of Applied and Engineering Mathematics 2010 TWMS Journal of Applied and Engineering Mathematics

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.

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