Disjunctive total domination in some tree networks

Vecdi Aytaç,Tufan Turacı

doi:10.26637/mjm904/003

Abstract

Networking has been an essential field of multidisciplinary study, including computational theory, mathematics, social sciences, computer science, and other theoretical and applied sciences. The vulnerability determines the network's resistance to interruption of information flow after the breakdown of particular stations or transmission connections. Recently, a new vulnerability parameter namely the disjunctive total domination number has been defined by Henning and Naicker [14]. This measure finds the critical vertices with an important position in the graph. In this context, we consider and compute exact formulae for the disjunctive total domination number in some tree networks.

Highlights

By γ(G) [3, 10]
New vulnerability parameter namely the disjunctive total domination number has been defined by Henning and Naicker [14]
The set S can be the disjunctive total dominating set of the graph G if and only if it satisfies any of the following properties

Summary

Introduction

By γ(G) [3, 10]. A total dominating set, abbreviated a TD-set, of a graph G, with no isolated vertex is a set S of vertices of G such that every vertex in V (G) is adjacent to at least one vertex in S. The disjunctive total domination number of G is the minimum cardinality of a DTD-set of G and denoted by γtd(G). Every TD-set is a DTD-set, the result γtd(G) ≤ γt(G) is obtained in [12,13,14]. We have γtd(G) ≥ 2 for any graph G by the definition of disjunctive total domination number.

Results

Conclusion