A complete characterisation of vertex-multiplications of trees with diameter 5
Autor: | Wong, W. H. W., Tay, E. G. |
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Rok vydání: | 2020 |
Předmět: | |
Zdroj: | Theory Appl. Graphs, 8, (2021), Article 6 |
Druh dokumentu: | Working Paper |
Popis: | Koh and Tay introduced a new family of graphs, $G$ vertex-multiplications, as an extension of complete $n$-partite graphs. They proved a fundamental classification of $G$ vertex-multiplications into three classes $\mathscr{C}_0, \mathscr{C}_1$ and $\mathscr{C}_2$. It was shown that any vertex-multiplication of a tree with diameter at least 3 does not belong to the class $\mathscr{C}_2$. Furthermore, for vertex-multiplications of trees with diameter $5$, some necessary and sufficient conditions for $\mathscr{C}_0$ were established. In this paper, we give a complete characterisation of vertex-multiplications of trees with diameter $5$ in $\mathscr{C}_0$ and $\mathscr{C}_1$. Comment: 9 pages |
Databáze: | arXiv |
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