Equitable Domination in Fuzzy Graphs

Abstract

Let G be a fuzzy graph. Let u and v be two vertices ofdenotes the degree of vertex u and deg(v) denotes the degree of vertex v and µ(uv) ≤ σ(u) ∧ σ(v). The minimum cardinality of a fuzzy equitable dominating set is denoted by γ ef . In this paper we introduce the concept of fuzzy equitable dominating set, minimal fuzzy equitable dominating set, strong (weak) fuzzy equitable dominating set , fuzzy equitable independent set and obtain some interesting results for this new parameter in equitable fuzzy graphs.

Domination of Fuzzy Incidence Graphs with the Algorithm and Application for the Selection of a Medical Lab

“…Ponnappan [22] et al proposed the novel idea of edge domination, total edge domination, the edge domination number, and the total edge domination number for certain classes of FGs. Dharmalingam and Rani [23] proposed an idea of equitable domination in FGs. Dharmalingam and Nithya [24,25] discussed the concept of excellent domination and very excellent domination in FGs.…”

“…Dharmalingam and Rani [23] proposed an idea of equitable domination in FGs. Dharmalingam and Nithya [24,25] discussed the concept of excellent domination and very excellent domination in FGs. Wang et al [26,27] addressed the H ∞ control and filtering problems for Markov jump singularity perturbed systems approximated by Takagi-Sugeno fuzzy models and stability analysis on singularity perturbed descriptor systems.…”

Equitable edge domination in vague graphs

“…They have defined equitable dominating set of a graph G as uv ∈ E(G) and | deg(u) − deg(v)| 1. K. M. Dharmalingam and M. Rani [4] have stated in detail fuzzy equitable minimal fuzzy equitable dominating set, dominating set, fuzzy equitable independent set of fuzzy graphs, strong or weak fuzzy equitable dominating set. A. Nagoor Gani and K. Prasanna Devi [8] introduced the notions of edge domination and fuzzy graph's independent edge dominating set.…”

Equitable edge domination in fuzzy graphs

“…Nagoorgani and Chandrasekaran [5] discussed about domination in a fuzzy graph using strong arcs. The concept of degree equitable domination in graphs was introduced by Venkatasubramanian Swaminathan and Kuppusamy Markandan Dharmalingam [8].Anwar Alwardi and Soner.N.D., [1] introduced equitable edge domination in graphs in the year 2013.The concept of equitable domination in fuzzy graphs was introduced by Dharmalingam and Rani [2]. We introduce the concept of paired equitable domination in fuzzy graph in 2018 [3].…”