Theoretical Computer Science ( IF 0.9 ) Pub Date : 2021-02-18 , DOI: 10.1016/j.tcs.2021.02.032 Canan Çiftçi
A subset is a disjunctive total dominating set if each vertex has a neighbor in S or has at least two vertices in S at distance two from it. The disjunctive total domination number is the minimum cardinality of a disjunctive total dominating set in G. Disjunctive total bondage number, , of a graph G with no isolated vertex is defined as the minimum cardinality of edge set whose deletion obtains a graph with no isolated vertex satisfying . If there is no such set B, it is then defined as . We, in this paper, present some bounds on disjunctive total bondage. Also, we prove that the disjunctive total bondage problem is NP-complete, even for bipartite graphs.
中文翻译:
析取性总束缚的复杂性和界限
一个子集 是分离性总控制集如果每个顶点具有在邻居小号或具有至少两个顶点小号在从中距离的两个。该析取总控制数 是G中析取性总支配集的最小基数。析取总束缚数,没有孤立顶点的图G的定义为边集的最小基数 其删除获得图 没有孤立的顶点令人满意 。如果没有这样的集合B,则将其定义为。在本文中,我们提出了析取总束缚的一些界限。此外,我们证明了析取的总束缚问题是NP完全的,即使对于二部图也是如此。