论文标题
直径为5
A complete characterisation of vertex-multiplications of trees with diameter 5
论文作者
论文摘要
Koh和Tay推出了一个新的图形系列，即$ G $ VERTEX-MULTIPLICATIONS，作为完整$ N $ - 分段图的扩展。他们证明了$ g $ vertex-multiplications的基本分类为$ \ mathscr {c} _0，\ mathscr {c} _1 $和$ \ mathscr {c} _2 $。结果表明，直径至少3的树的任何顶点 - 刺激性不属于$ \ Mathscr {C} _2 $。此外，对于直径$ 5 $的树木的顶点 - 刺激性，建立了一些$ \ mathscr {c} _0 $的必要条件。在本文中，我们给出了直径$ 5 $ in $ \ mathscr {c} _0 $和$ \ MATHSCR {C} _1 $的树木的顶点 - 杂物的完整表征。
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 $\mathscr{C}_1$.
