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arXiv · 1912.09604

The determinant of the distance matrix of graphs with at most two cycles

Ezequiel Dratman·Luciano N. Grippo·Matín D. Safe·Celso M. da Silva Jr.·Renata R. Del-Vecchio
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Abstract

Let $G$ be a connected graph on $n$ vertices and $D(G)$ its distance matrix. The formula for computing the determinant of this matrix in terms of the number of vertices is known when the graph is either a tree or {a} unicyclic graph. In this work we generalize these results, obtaining the determinant of the distance matrix for {all graphs} in a {class, including trees, unicyclic and bicyclic graphs. This class actually includes graphs with many cycles, provided that each block of the graph is at most bicyclic.}

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Ezequiel Dratman, Luciano N. Grippo, Matín D. Safe, Celso M. da Silva Jr., Renata R. Del-Vecchio. 2019-12-20. The determinant of the distance matrix of graphs with at most two cycles. https://arxiv.org/abs/1912.09604

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