The Maximum Edge Eccentricity Energy of a Graph

Articles in Press

Document Type : Research Paper

Authors

Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195--363, Semnan, Iran.

10.22128/gadm.2024.863.1119

Abstract

This paper presents a new concept in graph theory, focusing on a connected graph's edge eccentricity. We define a new matrix, the maximum edge eccentricity matrix $M_{e_{e}}(\Upsilon)$, which represents the maximum edge distance between all pairs of edges in the graph. This matrix is derived from the graph's structure and the eccentricity values of its edges. Our work explores the characteristics of this matrix, including the determination of specific coefficients within its characteristic polynomial, denoted as $P(\Upsilon,\nu)$. Furthermore, we introduce the concept of maximum edge eccentricity energy $M_{e_{e}}(\Upsilon)$ for connected graphs and provide calculations for well-known graphs. We establish upper and lower bounds for $E_{M_{e_{e}}}(\Upsilon)$ and prove that if the maximum edge eccentricity energy of a graph is rational, it must be an even number.

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References

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Analytical and Numerical Solutions for Nonlinear Equations

Articles in Press, Accepted Manuscript
Available Online from 03 November 2024

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History

  • Receive Date: 19 August 2024
  • Revise Date: 12 October 2024
  • Accept Date: 20 October 2024

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