REGULAR PARTIAL DOMATIC NUMBER ON ANTI FUZZY GRAPHS

Abstract

AG = (N, A, σ, μ) be a anti fuzzy graph. A partition of N(AG) Π = {D1, D2, …., Dk} is a regular anti fuzzy partial domatic partition of AG if (i) for each Di, is an anti fuzzy regular and (ii) Di is an anti fuzzy dominating set of GA. The maximum fuzzycardinality of a regular anti fuzzy partial domatic partition of AG is called the regular anti fuzzy partial domatic number [RAPDN]of AG and it is denoted by 𝑑𝑟𝑎𝑓(𝐴𝐺). Alsothese numbers are determined for various anti fuzzy graph. In this work, random rregular anti fuzzy graph, regular partial domatic number in anti fuzzy graphs, regular partial anti domatic number in anti fuzzy graphs are introduced. Some bounds for anti fuzzy domatic numbers are discussed.

Keywords

• anti fuzzy graph
• dominating set
• domatic number
• vertex degree.