ECCENTRICITY SPECTRUM OF JOIN OF CENTRAL GRAPHS AND ECCENTRICITY WIENER INDEX OF GRAPHS

Anjitha Ashokan; Chithra Av

ECCENTRICITY SPECTRUM OF JOIN OF CENTRAL GRAPHS AND ECCENTRICITY WIENER INDEX OF GRAPHS

Abstract

The eccentricity matrix of a simple connected graph is obtained from its distance matrix by preserving the largest non-zero distance in each row and column, while setting all other entries to zero. This article examines the $\epsilon$-spectrum and $\epsilon$-spectral radius of central graphs of triangle-free regular graphs. The study further explores the irreducibility of the eccentricity matrix of central graphs. Moreover, we investigate the $\epsilon$-spectrum and the irreducibility of various central graph operations, such as the central vertex join, central edge join, and central vertex-edge join. Also, we compute the $\epsilon$-energy of specific graphs. These findings allow us to construct new families of $\epsilon$-cospectral graphs and non $\epsilon$-cospectral $\epsilon$-equienergetic graphs. Additionally, we estimate certain upper and lower bounds for the eccentricity Wiener index of graphs and an upper bound for the eccentricity energy of self-centered graphs.

Keywords

Thanks

The authors would like to express their sincere gratitude to both the referees for a very careful reading of this paper and for all their insightful comments, which have led to several meaningful improvements.

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Details

Primary Language

English

Subjects

Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)

Journal Section

Research Article

Authors

Anjitha Ashokan This is me
0009-0000-1391-3085
India

Chithra Av ^*
0000-0003-3078-243X
India

Publication Date

June 9, 2026

Submission Date

April 24, 2025

Acceptance Date

September 17, 2025

Published in Issue

Year 2026 Volume: 16 Number: 6

IZ

https://izlik.org/JA86FX25MJ

Cite

RIS / Bibtex

APA

Ashokan, A., & Av, C. (2026). ECCENTRICITY SPECTRUM OF JOIN OF CENTRAL GRAPHS AND ECCENTRICITY WIENER INDEX OF GRAPHS. TWMS Journal of Applied and Engineering Mathematics, 16(6), 725-739. https://izlik.org/JA86FX25MJ

AMA

1.Ashokan A, Av C. ECCENTRICITY SPECTRUM OF JOIN OF CENTRAL GRAPHS AND ECCENTRICITY WIENER INDEX OF GRAPHS. JAEM. 2026;16(6):725-739. https://izlik.org/JA86FX25MJ

Chicago

Ashokan, Anjitha, and Chithra Av. 2026. “ECCENTRICITY SPECTRUM OF JOIN OF CENTRAL GRAPHS AND ECCENTRICITY WIENER INDEX OF GRAPHS”. TWMS Journal of Applied and Engineering Mathematics 16 (6): 725-39. https://izlik.org/JA86FX25MJ.

EndNote

Ashokan A, Av C (June 1, 2026) ECCENTRICITY SPECTRUM OF JOIN OF CENTRAL GRAPHS AND ECCENTRICITY WIENER INDEX OF GRAPHS. TWMS Journal of Applied and Engineering Mathematics 16 6 725–739.

IEEE

[1]A. Ashokan and C. Av, “ECCENTRICITY SPECTRUM OF JOIN OF CENTRAL GRAPHS AND ECCENTRICITY WIENER INDEX OF GRAPHS”, JAEM, vol. 16, no. 6, pp. 725–739, June 2026, [Online]. Available: https://izlik.org/JA86FX25MJ

ISNAD

Ashokan, Anjitha - Av, Chithra. “ECCENTRICITY SPECTRUM OF JOIN OF CENTRAL GRAPHS AND ECCENTRICITY WIENER INDEX OF GRAPHS”. TWMS Journal of Applied and Engineering Mathematics 16/6 (June 1, 2026): 725-739. https://izlik.org/JA86FX25MJ.

JAMA

1.Ashokan A, Av C. ECCENTRICITY SPECTRUM OF JOIN OF CENTRAL GRAPHS AND ECCENTRICITY WIENER INDEX OF GRAPHS. JAEM. 2026;16:725–739.

MLA

Ashokan, Anjitha, and Chithra Av. “ECCENTRICITY SPECTRUM OF JOIN OF CENTRAL GRAPHS AND ECCENTRICITY WIENER INDEX OF GRAPHS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 6, June 2026, pp. 725-39, https://izlik.org/JA86FX25MJ.

Vancouver

1.Anjitha Ashokan, Chithra Av. ECCENTRICITY SPECTRUM OF JOIN OF CENTRAL GRAPHS AND ECCENTRICITY WIENER INDEX OF GRAPHS. JAEM [Internet]. 2026 Jun. 1;16(6):725-39. Available from: https://izlik.org/JA86FX25MJ