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引用次数: 6
摘要
连通图G的弱连通2-支配集是一个集D≠V (G),其中V (G)\D中的每个顶点与D中的至少两个顶点相邻,且由D弱诱导的子图< D > w是连通的。本文对图的连接G + H和K1 + H中的弱连通2-控制集进行了刻画,得到了它们对应的弱连通2-控制数。给出了图的连接具有弱连通2-控制数等于2、3、4的充分必要条件。数学学科分类:05C69
Weakly connected 2-domination in the join of graphs
A weakly connected 2-dominating set of a connected graph G is a set D ⊆ V (G) such that every vertex in V (G)\D is adjacent to at least two vertices in D and the subgraph, 〈D〉w, weakly induced by D is connected. In this paper, the weakly connected 2-dominating sets in the join G + H and K1 + H of graphs are characterized and their corresponding weakly connected 2-domination numbers are obtained. The necessary and sufficient conditions for the join of graphs to have weakly connected 2-domination numbers equal to 2,3 and 4 are provided. Mathematics Subject Classification: 05C69
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