Information Processing Letters ( IF 0.5 ) Pub Date : 2020-10-27 , DOI: 10.1016/j.ipl.2020.106062 Jie Chen , Shou-Jun Xu
A subset S of vertices in a graph G with vertex set V and edge set E is a dominating set of G if every vertex of is adjacent to a vertex in S. The minimum cardinality of a dominating set is the dominating number of G. G is a 3-γ-critical graph if and for ; G is bicritical if contains a perfect matching for every pair of distinct vertices . In this paper, we characterize 3-connected 3-γ-critical graphs G of even order which are not bicritical: two classes of graphs, which generalizes the result: if the minimum degree of G is at least 4, then G is bicritical N. Ananchuen and M.D. Plummer (2014) [2].
中文翻译:
非双临界的3- γ临界图的特征
一个子集小号在图中的顶点的ģ与顶点组V和边缘集Ë是一个控制集的ģ如果每个顶点的与S中的顶点相邻。支配集的最小基数是支配数 的ģ。如果是,则G是一个3 -γ临界图 和 对于 ; 如果G是双临界的 包含每对不同顶点的完美匹配 。在本文中,我们刻画了非双临界的偶数阶3连通3- γ临界图G:两类图,将结果概括如下:如果G的最小度至少为4,则G为双临界N Ananchuen和MD Plummer(2014)[2]。