Key points are not available for this paper at this time.
One area of graph theory that has been studied in great detail is dominance in graphs. Applications for dominating sets are numerous. In wireless networking, dominant sets are used to find effective paths inside ad hoc mobile networks. They have also been used in the creation of document summaries and safe electrical grid systems. A set IS/I⊆IV/I is said to be dominating set of IG/I if for every iv /iє IV/I-IS/I there exists a vertex iu/i є IS/I such that iuv/i є IE/I. The dominance number of IG/I, represented by iγ/i(IG/I), is the lowest cardinality of vertices among the dominating set of IG/I. A classic NP-complete decision problem in computational complexity theory determines whether, given a graph IG/I and input IK/I, iγ/i(IG/I) ≤ IK/I. This is known as the dominating set issue. Consequently, it is thought that calculating iγ/i(IG/I) for each given graph IG/I may not be possible to do with a feasible algorithm. In addition to efficient approximation tactics, there exist efficient exact techniques for various graph classes. If there are no neighboring vertices in a subset IS/I, then IS/I⊆IV/I is an independent set. Additionally, the empty set and the subset with just one vertex are independent. An independent dominating set of IG/I is a set IS/I of vertices in a graph IG/I that is both an independent and a dominating set of IG/I. This papers primary goal is to investigate the dominance and independent dominating set of many graphs, including the line graph, the alternate triangular belt graph, the bistar graph, the triangular snake graph, and others.
Mohamed et al. (Fri,) studied this question.