Hinge Total Domination on Some Graph Families

setSof vertices in a graphG= (V(G),E(G)) is a hinge dominating set if every vertexu∈VrSis adjacent to some vertexv∈Sand a vertexw∈VrSsuch that (v,w) is not an edgeinE(G). The hinge domination numberγh(G) is the minimum size of a hinged dominating set.A setSis called a total dominating set ofGif for every vertex inV, including those inSisadjacent to at least one vertex inS. The cardinality of a minimum total dominating set inGiscalled the total domination number ofGand denoted asγt(G). In this study, a new parametercalled hinged total dominating set was introduced and defined as, a hinge total dominating setof a graphGis a setSof vertices ofGsuch thatSis both a hinge dominating set and totaldominating set. The hinge total domination number,γht(G), is the minimum cardinality of ahinge total dominating set ofG. We initiate a study of hinge total dominating set and presentits characterization. In addition, we also determine the exact values of hinge total dominationnumber on some graph families.