直径为5的树的顶点倍增的一个完全刻画
A complete characterisation of vertex-multiplications of trees with diameter 5
摘要：
Koh和Tay引入了一个新的图族，$G$顶点乘法，作为完全$n$ -部图的扩展。他们证明了$G$顶点乘法的基本分类分为三类$\mathscr{C}_0, \mathscr{C}_1$和$\mathscr{C}_2$。证明了直径至少为3的树的顶点乘法不属于类$\mathscr{C}_2$。此外，对于直径为$5$的树的顶点增殖，给出了$\mathscr{C}_0$的一些充要条件。本文在$\mathscr{C}_0$和$\mathscr{C}_1$中给出了直径为$5$的树的顶点乘法的完整刻画。
英文摘要：
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 $\mathscr{C}_1$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
