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arXiv · 1810.04870

Path matrix and path energy of graphs

Aleksandar Ilic·Milan Basic
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Abstract

Given a graph $G$, we associate a path matrix $P$ whose $(i, j)$ entry represents the maximum number of vertex disjoint paths between the vertices $i$ and $j$, with zeros on the main diagonal. In this note, we resolve four conjectures from [M. M. Shikare, P. P. Malavadkar, S. C. Patekar, I. Gutman, \emph{On Path Eigenvalues and Path Energy of Graphs}, MATCH Commun. Math. Comput. Chem. {\bf 79} (2018), 387--398.] on the path energy of graphs and finally present efficient $O(|E| |V|^3)$ algorithm for computing the path matrix used for verifying computational results.

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Aleksandar Ilic, Milan Basic. 2018-10-11. Path matrix and path energy of graphs. https://arxiv.org/abs/1810.04870

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