论文标题
中间图的总统治数
Total domination number of middle graphs
论文作者
论文摘要
没有孤立顶点的图G的总统治集是顶点集的一个子集S，使得G的每个顶点与S VERTEX相邻。G的总统治数是G。G的总统治集的最小基数。在本文中，我们研究了中间图的总统治数。确实，我们根据图G的顺序获得了此数字的紧密界限。我们还明确计算了一些已知图的中间图的总统治数。此外，在中间图的总统治数中提出了一些Nordhaus-gaddum样关系。
A total dominating set of a graph G with no isolated vertices is a subset S of the vertex set such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set of G. In this paper, we study the total domination number of middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph G. We also compute the total domination number of the middle graph of some known families of graphs explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the total domination number of middle graphs.
