Volume 72 | Issue 3 | Year 2026 | Article Id. IJMTT-V72I3P105 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I3P105
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 18 Jan 2026 | 23 Feb 2026 | 14 Mar 2026 | 27 Mar 2026 |
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
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.
[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]