Strong weak domination and domination balance in a graph

Strong weak domination and domination balance in a graph

Let G = (V, E) be a graph and u, v ~ V. Then, u strongly dominates v and v weakly dominates u if (i) uv ~ E and (ii) deg u >/deg v. A set D c V is a strong-dominating set (sd-set) of G if every vertex in V D is strongly dominated by at least one vertex in D. Similarly, a weak-dominating set (wd-set) is defined. The strong (weak) domination number 7s (7w) of G is the minimum cardinality of an sd...

Total Strong (Weak) Domination Intuitionistic Fuzzy Graph

Strong (Weak) Edge-Edge Domination Number of a Graph

For any edge of an isolate free graph , , 〈 〉 is the subgraph induced by the vertices adjacent to u and v in G. We say that an edge x, edominates an edge y if ∈ 〈 〉 . A set ⊆ is an Edge-Edge Dominating Set (EED-set) if every edge in is e-dominated by an edge in L. The edgeedge domination number is the cardinality of a minimum EED-set. We find the relation ship between the new parameter and some...

Total Semi - μ Strong (Weak) Domination in Intuitionistic Fuzzy Graph

In the initial stage we proposed the concept of Total Strong (Weak) domination in Fuzzy graph. It deal with the real time application that helps a individual person in crossing a road traffic signal. We will be giving a single value for vertices and edges. Enhancing the same concept, the Total Strong (Weak) domination in Intuitionistic Fuzzy graph was proposed. Here we will be giving a double v...

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...