فهرست نشریات علمی دسترسی آزاد ایران

In a graph G = (V, E) with no isolated vertices, a subset D of vertices is said to be a total dominating set (abbreviated TDS) if it has the property that every vertex of G is adjacent to some vertex in D. A TDS D is said to be a total restrained dominating set (abbreviated TRDS) if it has a further property that any vertex in V-D is also adjacent to a vertex in V-D. Given the isolate-free graph G, the total restrained domination number of G, which we denote it by γtr(G), is the minimum cardinality of a TRDS of G. The minimum number of vertices of the graph G whose removal changes the total restrained domination number of G is called the total restrained domination stability number of G, and is denoted by stγtr(G). In this paper we study this variant in bipartite graphs. We show that the related decision problem related to this variant is NP-hard in bipartite graphs. We also determine the total restrained stability number in some families of graphs, including the families of trees and unicyclic graphs.