...

  • Home
  • Articles
    • Current Issue
    • Archives
  • Authors
    • Author Guidelines
    • Policies
    • Downloads
  • Editors
  • Reviewers
...

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 3 | Year 2026 | Article Id. IJMTT-V72I3P105 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I3P105

Computing Spectra and Product Eccentricity Energy of the Cartesian Product of K2 and Cycle Graphs


Priya Karen S, Arokia Lancy A
Received Revised Accepted Published
18 Jan 2026 23 Feb 2026 14 Mar 2026 27 Mar 2026
Citation :

Priya Karen S, Arokia Lancy A, "Computing Spectra and Product Eccentricity Energy of the Cartesian Product of K2 and Cycle Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 3, pp. 40-48, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I3P105

Abstract

This article investigates the product eccentricity energy of the Cartesian product of 𝒦2 and 𝒞𝔫. While spectral graph theory has extensively covered adjacency and Laplacian energies of product graphs, there remains a research gap in understanding how eccentricity-based spectra behave under graph operations. By leveraging established results in spectral graph theory, product eccentricity energy of cycle graphs, and illustrations on the Cartesian product of 𝒦2 and 𝒞𝔫 ,𝔫 ≥ 3 are given. 

Keywords
Cartesian Product, Complete Graph K2, Cycle Graphs, Product Eccentricity Energy, Spectrum.
References

[1] D. B. West, Introduction to Graph Theory, 2nd ed., Upper Saddle River, NJ: Prentice Hall, 2001.
[
Google Scholar] [Publisher Link]

[2] Serge Lang, Algebra, 3rd ed., New York, NY: Springer, 2002.
[CrossRef] [Google Scholar] [Publisher Link]

[3] D.M. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs: Theory and Application, New York, NY: Academic Press, vol. 87, 1980.
[
Google Scholar] [Publisher Link]

[4] Mustapha Aouchiche, and Pierre Hansen, “Distance Spectra of Graphs: A Survey,” Linear Algebra and its Applications, vol. 458, pp. 301–386, 2014.
[
CrossRef] [Google Scholar] [Publisher Link]

[5] N. Prabhavathy, “A New Concept of Energy from Eccentricity Matrix of Graphs,” Malaya Journal of Matematik, vol. S, no. 1, pp. 400-402, 2019.
[
CrossRef] [Google Scholar] [Publisher Link]

[6] I. Gutman, “The Energy of a Graph,” Ber. Math.-Statist. Sekt. Forsch. Graz, vol. 103, pp. 1-22, 1978. 
[Google Scholar]

[7] Xueliang Li, Yongtang Shi, and Ivan Gutman, Graph Energy, New York: Springer, 2012.
[
CrossRef] [Google Scholar] [Publisher Link]

[8] C. Adiga, and M. Smitha, “On Maximum Degree Energy of a Graph,” International Journal of Contemporary Mathematical Sciences, vol. 4, no. 8, pp. 385-396, 2009.
[
Google Scholar] [Publisher Link]

[9] Milan Randić, “DMAX-Matrix of Dominant Distances in a Graph,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 70, pp. 221–238, 2013.
[
Google Scholar] [Publisher Link]

[10] M. Ahmed Naji, and N. D. Soner, “The Maximum Eccentricity Energy of a Graph,” International Journal of Scientific & Engineering Research, vol. 7, no. 5, pp. 5-13, 2016.
[
Google Scholar]

[11] Mohammad Issa Sowaity, and B. Sharada, “The Sum-Eccentricity Energy of a Graph,” International Journal on Recent and Innovation Trends in Computing and Communication, vol. 5, no. 6, pp. 293-304, 2017.
[
CrossRef] [Google Scholar] [Publisher Link]

[12] Andries E. Brouwer, and Willem H. Haemers, Spectra of Graphs, New York: Springer, 2011.
[
CrossRef] [Google Scholar] [Publisher Link]

[13] S. Priya Karen, and A. Arokia Lancy, “Product Eccentricity Energy of Various Graphs Using Its Eigen Values,” International Journal of Applied Graph Theory, vol. 9, no. 1, pp. 1-8, 2025.
[
Publisher Link]

[14] S. Avgustinovich, and D. Fon-der-flaass, “Cartesian Products of Graphs and Metric Spaces," European Journal of Combinatorics, vol. 22, no. 6, pp. 847-851, 2001.
[
CrossRef] [Google Scholar] [Publisher Link]

[15] Dragoš Cvetković, Peter Rowlinson, and Slobodan Simić, An Introduction to the Theory of Graph Spectra, Cambridge, UK: Cambridge University Press, 2010.
[
Google Scholar] [Publisher Link]

  • PDF
  • Citation
  • Abstract
  • Keywords
  • References
Citation Abstract Keywords References
  • Home
  • Authors Guidelines
  • Paper Submission
  • APC
  • Archives
  • Downloads
  • Open Access
  • Publication Ethics
  • Copyrights Infringement
  • Journals
  • FAQ
  • Contact Us

Follow Us

Copyright © 2026 Seventh Sense Research Group® . All Rights Reserved