ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS

Surya S; Pramada Ramachandran

ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS

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

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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Details

Primary Language

English

Subjects

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Journal Section

Research Article

Authors

Surya S ^* This is me
0009-0003-7976-4299
India

Pramada Ramachandran This is me
0000-0001-8647-0000
India

Publication Date

April 7, 2026

Submission Date

March 13, 2025

Acceptance Date

June 23, 2025

Published in Issue

Year 2026 Volume: 16 Number: 4

IZ

https://izlik.org/JA56WH77AS

Cite

RIS / Bibtex

APA

S, S., & Ramachandran, P. (2026). ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS. TWMS Journal of Applied and Engineering Mathematics, 16(4), 521-535. https://izlik.org/JA56WH77AS

AMA

1.S S, Ramachandran P. ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS. JAEM. 2026;16(4):521-535. https://izlik.org/JA56WH77AS

Chicago

S, Surya, and Pramada Ramachandran. 2026. “ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS”. TWMS Journal of Applied and Engineering Mathematics 16 (4): 521-35. https://izlik.org/JA56WH77AS.

EndNote

S S, Ramachandran P (April 1, 2026) ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS. TWMS Journal of Applied and Engineering Mathematics 16 4 521–535.

IEEE

[1]S. S and P. Ramachandran, “ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS”, JAEM, vol. 16, no. 4, pp. 521–535, Apr. 2026, [Online]. Available: https://izlik.org/JA56WH77AS

ISNAD

S, Surya - Ramachandran, Pramada. “ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS”. TWMS Journal of Applied and Engineering Mathematics 16/4 (April 1, 2026): 521-535. https://izlik.org/JA56WH77AS.

JAMA

1.S S, Ramachandran P. ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS. JAEM. 2026;16:521–535.

MLA

S, Surya, and Pramada Ramachandran. “ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 4, Apr. 2026, pp. 521-35, https://izlik.org/JA56WH77AS.

Vancouver

1.Surya S, Pramada Ramachandran. ECCENTRICITY SPECTRA OF SOME GRAPH OPERATIONS IN REGULAR GRAPHS. JAEM [Internet]. 2026 Apr. 1;16(4):521-35. Available from: https://izlik.org/JA56WH77AS