2-Secure Domination in Bipolar Hesitancy Fuzzy Graph

Total strong (weak) domination in bipolar fuzzy graph

In this paper, the new kind of parameter strong (weak) domination number in a bipolar fuzzy graph is defined and established the parametric conditions. Another new kind of parameter a totalstrong (weak) bipolar domination number is defined and established the parametric conditions. The properties of strong (weak) bipolar domination number and totalstrong (weak) bipolar domination numbersare dis...

Edge criticality in secure graph domination

The domination number of a graph is the cardinality of a smallest subset of its vertex set with the property that each vertex of the graph is in the subset or adjacent to a vertex in the subset. This graph parameter has been studied extensively since its introduction during the early 1960s and finds application in the generic setting where the vertices of the graph denote physical entities that...

Edge stability in secure graph domination

A subset X of the vertex set of a graph G is a secure dominating set of G if X is a dominating set of G and if, for each vertex u not in X, there is a neighbouring vertex v of u in X such that the swap set (X − {v}) ∪ {u} is again a dominating set of G. The secure domination number of G is the cardinality of a smallest secure dominating set of G. A graph G is p-stable if the largest arbitrary s...

Some results on Bipolar Fuzzy Graph

In this paper, the notion ofgraph operationsdisjunction and symmetric difference on bipolar fuzzy graphs are defined and it is proved that the new graph is a bipolar graph. Furthermore,the new concepts of bipolar fuzzy graphs calledupperstrong and lower strongbipolar fuzzy graphare introduced and some related </...

Total Strong (Weak) Domination Intuitionistic Fuzzy Graph