Some More Results on Total Equitable Bondage Number of A Graph

Abstract

The bondage number of a nonempty graph is the minimum cardinality among all sets of edges for which . An equitable dominating set is called a total equitable dominating set if the induced subgraph has no isolated vertices. The total equitable domination number of is the minimum cardinality of a total equitable dominating set of . If and contains no isolated vertices then the total equitable bondage number of a graph is the minimum cardinality among all sets of edges for which . In the present work we prove some characterizations and investigate total equitable bondage number of Ladder and degree splitting of path.

Restrained Edge Domination Number of Some Path Related Graphs

“…Restrained domination in the context of path and cycle is discussed by Vaidya and Ajani [7,8] while the restrained domination of complete graph, multipartite graphs and the graphs with minimum degree two is well studied by Domke et al [9,10]. Moreover the concept of total equitable bondage number was introduced by Vaidya and Parmar [11,12] while equi independent equitable domination was explored by Vaidya and Kothari [13]. These variants are introduced by identifying one or more characteristics of elements of vertex subset or edge subset.…”