Coulson integral formula for the vertex energy of a graph

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Arizmendi, Octavio; Olivera, Beatriz Carely Luna; Ibáñez, Marcelino Ramírez;

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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