Path matrix and path energy of graphs
| Autor: | Ilic, Aleksandar, Basic, Milan |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 8 pages |
| Databáze: | arXiv |
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