Closed Fuzzy Dominating Set in Fuzzy Graphs

Fuzzy Forcing Set on Fuzzy Graphs

The investigation of impact of fuzzy sets on zero forcing set is the main aim of this paper. According to this, results lead us to a new concept which we introduce it as Fuzzy Zero Forcing Set (FZFS). We propose this concept and suggest a polynomial time algorithm to construct FZFS. Further more we compute the propagation time of FZFS on fuzzy graphs. This concept can be more efficient to model...

Strength of strongest dominating sets in fuzzy graphs

A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...

Equitable Dominating in an Intunionistic Fuzzy Graphs

Let G be an intuitionistic fuzzy graph. Let u and v be two vertices of G. A subset D of V is called a fuzzy equitable dominating set if every v ∈ V − Dthere exist a vertex u ∈ D such that uv ∈ E(G) and |deg(u) − deg(v)| = 1 where deg(u) denotes the degree of vertex u and deg(v) denotes the degree of vertex v and μ2(vi, vj ) = μ1(vi) ∧ μ1(vj ), γ2(vi, vj ) = γ1(vi) ∨ γ1(vj ). The minimum cardina...

Dominating Critical in Intuitionistic Fuzzy Graphs

Let G be an IFG. Then V D  is said to bae a strong (weak) dominating set if every D V v   is strongly (weakly) dominated by some vertex in D. We denote the strong (weak) intuitionistic fuzzy dominating set by sid-set (wid-set). The minimum vertex cardinality over all the sid-set (wid-set) is called the strong (weak) dominating number of an IFG and is denoted by )] ( [ ) ( G G wid sid   In ...

Dominating Critical in Intuitionistic Fuzzy Graphs