Excellent Domination Fuzzy Graphs
K. M. Dharmalingam, P. Nithya · Philologist – Journal Of Langugage, Literary And Cultural Studies (University of Banja Luka) · 2016
Let G be a fuzzy graph.A subset D of V is said to be Fuzzy dominating set if every vertex u ∈ V (G) there exists a vertex v ∈ V -D such that uv ∈ E(G) and µ(uv) σ(u) ∧ σ(v).The minimum Cardinality of fuzzy dominating set is denoted by γ f .A graph G is said to be fuzzy excellent if every vertex of G belongs to γ f -sets of G.In this paper, we give a construction to imbedded non-excellent fuzzy graph G in an excellent fuzzy graph H such that γ f (H) γ f (G) + 2. We also show that for a given non-excellent fuzzy graph G, there is subdivision of G which is fuzzy excellent.Also, we introduce the concept of γ f -flexible, fuzzy bridge independent dominating number γ f b i and obtain some interesting results for this new parameter in excellent fuzzy graphs.