Coulson Integral Formula for the Vertex Energy of a Graph
Octavio Arizmendi, Beatriz Carely Luna Olivera, Marcelino Ram\'irez, Ib\'a\~nez
TL;DR
This paper derives a Coulson integral formula to compute the vertex energy of a graph, providing a new analytical tool and demonstrating its application to bipartite graphs.
Contribution
It introduces a Coulson integral formula for vertex energy, offering a novel analytical approach and practical examples, especially for bipartite graphs.
Findings
Derived Coulson integral formula for vertex energy
Applied the formula to bipartite graphs
Provided examples demonstrating the formula's use
Abstract
In this note we prove that the vertex energy of a graph, as defined in Arizmendi and Juarez (2018), can be calculated in terms of a Coulson integral formula. We present examples of how this formula can be used, and we show some applications to bipartite graphs.
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