On Total Domination in some Path Related Graphs

Some More Results on Total Equitable Bondage Number of A Graph

“…We have introduced the concept of total equitable bondage number in reference [8]. Here we have explored the same concept.…”

“…In this situation, total domination is useful while there is no difference of opinion between any two members or they differ on at most one issue then the concept of equitable domination is applicable. A concept with both the blends is termed as total equitable dominating set was introduced by Basavanagoud et al [6] and further formalized by Vaidya and Parmar [7][8][9][10]. Using the framework of total equitable dominating sets, we have introduced a new concept called total equitable bondage number [11].…”

Domination Integrity of Some Special Graphs

“…The Domination integrity of a connected graph G is written as [9] studied the domination integrity of duplication of a vertex(or an edge) by an edge(or vertex), Splitting graph of path and cycle, and Splitting and degree splitting graph of some graphs. The domination integrity of Shadow graphs of bistar, path, complete bipartite and cycle, some path related graphs and total graphs of star, path and cycle graphs were analyzed by Shah and Vaidya [10]- [12]. Veena and Sulthan seena [6] have investigated the domination integrity of Line Splitting and central graph of some standard graphs.…”

On total domination and total equitable domination in graphs

“…The total equitable domination number of G is the minimum cardinality of a total equitable dominating set of G which is denoted by γ e t (G). This concept was introduced by Basavanagoud et al [2] and further explored by Vaidya and Parmar [11,12]. The concept of total equitable bondage number possesses the blend of total equitable domination as well as bondage number in graphs.…”