A complete characterisation of vertex-multiplications of trees with diameter 5

Autor:	Wong, W. H. W., Tay, E. G.
Rok vydání:	2020
Předmět:	Mathematics - Combinatorics 05C12 05C20 G.2.2 F.2.2
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
Externí odkaz:	http://arxiv.org/abs/2007.06399 Zobrazit plný text záznamu View this record from Arxiv