论文标题
非 - 非 - 非透明顶点传递图的总颜色和有效的统治应用
Total coloring and efficient domination applications to non-Cayley non-Shreier vertex-transitive graphs
论文作者
论文摘要
令$ 0 <k \ in \ mathbb {z} $。让Star 2-SET换位图$ ST^2_k $为$（2K-1）$ - 常规图，其顶点是$ K $符号上的$ 2K $ - 符号，每个符号重复两次，每个符号的边缘由一个$ 2K $ string的初始输入（包含任何一个不同的符号）的初始输入的初始输入，其每个符号都与初始条目相比。煎饼2-set换位图$ pc^2_k $具有相同的顶点集$ st^2_k $及其边缘，其边缘涉及每个Endvertex字符串前缀的同心偏置换位的最大产物，包括外部换位，包括$ st^2_k $的边缘。对于$ 1 <k \ in \ mathbb {z} $，我们表明$ st^2_k $和$ pc^2_k $，除其他中间转置图外，还具有$ 2K-1 $颜色的总颜色。 They, in turn, yield efficient dominating sets, or E-sets, of the vertex sets of $ST^2_k$ and $PC^2_k$, and partitions into into $2k-1$ such E-sets, generalizing Dejter-Serra work on E-sets in such graphs.
Let $0<k\in\mathbb{Z}$. Let the star 2-set transposition graph $ST^2_k$ be the $(2k-1)$-regular graph whose vertices are the $2k$-strings on $k$ symbols, each symbol repeated twice, with its edges given each by the transposition of the initial entry of one such $2k$-string with any entry that contains a different symbol than that of the initial entry. The pancake 2-set transposition graph $PC^2_k$ has the same vertex set of $ST^2_k$ and its edges involving each the maximal product of concentric disjoint transpositions in any prefix of an endvertex string, including the external transposition being that of an edge of $ST^2_k$. For $1<k\in\mathbb{Z}$, we show that $ST^2_k$ and $PC^2_k$, among other intermediate transposition graphs, have total colorings via $2k-1$ colors. They, in turn, yield efficient dominating sets, or E-sets, of the vertex sets of $ST^2_k$ and $PC^2_k$, and partitions into into $2k-1$ such E-sets, generalizing Dejter-Serra work on E-sets in such graphs.
