论文标题
边缘确定集合并确定索引
Edge Determining Sets and Determining Index
论文作者
论文摘要
图形自动形态是维持相邻顶点的顶点的徒图。确定图的顶点是一组顶点，因此唯一修复这些顶点的自动形态是身份。最小的集合的大小称为确定数字，表示为det $（g）$。确定数是图捕获其对称水平的图的参数。我们介绍了边缘确定集合和确定索引的相关概念，det $'（g）$。我们证明det $'（g）\ le \ text {det}（g）\ le 2 \ text {det}'（g）$当det $（g）\ neq 1 $ $，并且显示两个范围对于无限的图形系族。此外，我们研究了这些新概念的特性，并为几个图的家族提供了确定索引。
A graph automorphism is a bijective mapping of the vertices that preserves adjacent vertices. A vertex determining set of a graph is a set of vertices such that the only automorphism that fixes those vertices is the identity. The size of a smallest such set is called the determining number, denoted Det$(G)$. The determining number is a parameter of the graph capturing its level of symmetry. We introduce the related concept of an edge determining set and determining index, Det$'(G)$. We prove that Det$'(G) \le \text{Det}(G) \le 2\text{Det}'(G)$ when Det$(G) \neq 1$ and show both bounds are sharp for infinite families of graphs. Further, we investigate properties of these new concepts, as well as provide the determining index for several families of graphs.
