Affiliations: [a] Department of Mathematics, Faculty of Arts and Sciences, Ordu University, 52200, Ordu, Turkey. cananciftci@odu.edu.tr | [b] Department of Computer Engineering, Faculty of Engineering, Ege University, 35100, Izmir, Turkey. vecdi.aytac@ege.edu.tr
Correspondence:
[*]
Address for correspondence: Department of Computer Engineering, Faculty of Engineering, Ege University, 35100, Izmir, Turkey.
Abstract: A set S ⊆ V (G) is a disjunctive total dominating set of G if every vertex has a neighbor in S or has at least two vertices in S at distance 2 from it. The disjunctive total domination number is the minimum cardinality of a disjunctive total dominating set in G. We define the disjunctive total domination subdivision number of G as the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) to increase the disjunctive total domination number. In this paper, we first study the disjunctive total domination subdivision number of some special graphs. Next, we give some upper bounds on the disjunctive total domination subdivision number for any graphs in terms of vertex degree. Finally, we supply some conditions for a graph G to have a minimum disjunctive total domination subdivision number.
Keywords: domination, disjunctive total domination, subdivision
