论文标题
笛卡尔产品的最佳顶点 - 形式的最佳取向
Optimal orientations of vertex-multiplications of cartesian products of graphs
论文作者
论文摘要
KOH和TAY证明了$ G $ VERTEX-MULTIPICATIONS的基本分类为三个类$ \ Mathscr {C} _0，\ Mathscr {C} _1 $和$ \ Mathscr {C} _2 $。在本文中，我们证明了$ \ times h $ tim in $ \ mathscr {c} _0 $（$ \ mathscr {c} _0 \ cup \ cup \ mathscr {c} _1 $ rest。 （$ \ mathscr {c} _1 $ resp。），$ d（g）\ ge 2 $和$ d（g \ times h）\ ge 4 $。我们还专注于涉及树木，路径和周期的笛卡尔产品，并表明其中大多数位于$ \ Mathscr {C} _0 $中。
Koh and Tay proved a fundamental classification of $G$ vertex-multiplications into three classes $\mathscr{C}_0, \mathscr{C}_1$ and $\mathscr{C}_2$. In this paper, we prove that vertex-multiplications of cartesian products of graphs $G\times H$ lie in $\mathscr{C}_0$ ($\mathscr{C}_0\cup \mathscr{C}_1$ resp.) if $G^{(2)}\in \mathscr{C}_0$ ($\mathscr{C}_1$ resp.), $d(G)\ge 2$ and $d(G\times H)\ge 4$. We also focus on cartesian products involving trees, paths and cycles and show that most of them lie in $\mathscr{C}_0$.
