Strong Split Independent Domination in Fuzzy Graphs - P. Gladyis; C. V. R. Harinarayanan; R. Muthuraj (International Journal of Mathematics And its Applications, 2016)
An independent dominating set D of a fuzzy graph $G=(σ, μ)$ is a split dominating set if the induced subgraph $H=(\langle V-D\rangle, σ', μ')$ is disconnected. The minimum of the fuzzy cardinalities of a split independent dominating sets of G is called the split independent domination number $γ_{sif}(G)$ of G. An independent dominating set D of a fuzzy graph $G=(σ, μ)$ is a strong split independent dominating set if the induced subgraph $H=(\langle V-D\rangle, σ', μ')$ is totally disconnected. The minimum of the fuzzy cardinalities of a strong split independent dominating sets of G is called the strong split independent domination number $γ_{ssif}(G)$ of G. In this paper we study a strong split independent dominating sets of fuzzy graphs and investigate the relationship of $γ_{ssif}(G)$ or $γ_{ssif}$ with other known parameter of G.