Authors:
R. Nayana, M. Rajeshwari

Addresses:
Department of Mathematics, Presidency University, Bengaluru, Karnataka, India.

Abstract:

In this work, the primary focus is on the investigation of the Total Eccentricity Polynomial, which is generated from the Cartesian product of Unitary Cayley graphs and important standard graphs. These graphs include path, star, wheel, friendship, full binomial tree helm, crown, Pl_n, double star, and grid graphs. In addition to elucidating the development of graphs through the Cartesian product, it offers a straightforward explanation of how the polynomial is developed. In addition, it provides a detailed, step-by-step study of how eccentricity, diameter, radius, and vertex degree in each graph affect the development of the Cartesian product and the role the function plays in defining the coefficients in the Total Eccentricity Polynomial. This polynomial serves as a general tool for graphs obtained from the Cartesian product. It also paves the way for further research that uses various graph products from the literature, including other standard graphs. As a result, it presents a substantial potential for applications in related mathematical and computational domains through these innovative considerations.

Keywords: Cartesian Product; Graph Polynomials; Total Eccentricity Polynomial; Unitary Cayley Graphs; Standard Graphs; Local Structure; Product Graphs; Eccentricity Metrics.

Received on: 13/06/2024, Revised on: 31/08/2024, Accepted on: 29/12/2024, Published on: 05/12/2025

DOI: 10.69888/FTSASS.2025.000567

FMDB Transactions on Sustainable Applied Sciences, 2025 Vol. 2 No. 2, Pages: 75-86

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