Disjunctive Total Domination Subdivision Number of Graphs

Disjunctive Total Domination of Some Shadow Distance Graphs

“…For a set S ⊆ V (G), if each vertex is adjacent to a vertex in S or has at least two vertices in S at distance two from it, then the set S is a disjunctive total dominating set, briefly DTD-set, of G. When a vertex u satisfies one of these two conditions, it is known that u is disjunctively totally dominated, briefly DT-dominated, by vertices of S. Furthermore, when u satisfies the first condition (the second condition, respectively), it is known that u is totally dominated (disjunctively dominated, respectively) by vertices of S. The disjunctive total domination number, γ d t (G), is the minimum cardinality of a DTD-set in G. A DTD-set which gives the value γ d t (G) is called γ d t (G)-set. This parameter is studied on grids, trees, permutation graphs, claw-free graphs and it is applied on some graph modifications such as bondage and subdivision [6]- [12]. This paper is about disjunctive total domination number of shadow distance graph of some special graphs.…”

Disjunctive total domination stability in graphs

“…In this paper, we introduce the same concept for disjunctive total domination. For detailed information and results regarding disjunctive total domination, we refer interested readers to the papers [23][24][25][26] and references therein.…”