In this paper, d m -degree and total d m -degree of a vertex in fuzzy graphs, m-neighbourly irregular fuzzy graphs and m-neighbourly totally irregular fuzzy graphs are introduced. Some properties on m-neighbourly irregular fuzzy graphs are also discussed in this paper. Comparative study between m-neighbourly irregular fuzzy graphs and m-neighbourly totally irregular fuzzy graphs is done and m-neighbourly irregularity on some fuzzy graphs whose underlying crisp graphs are a cycle and a path is

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... so studied. also discussed some properties on m-neighbourly irregular fuzzy graphs. We make comparative study between m-neighbourly irregular fuzzy graphs and m-neighbourly totally irregular fuzzy graphs. Also m-neighbourly irregularity on some fuzzy graphs whose underlying crisp graphs are a cycle and a path is studied. Preliminaries We present some known definitions and results for a ready reference to go through the work presented in this paper. Definition 2.1. A Fuzzy graph denoted by G : (σ, µ) on the graph G * : (V, E) is a pair of functions (σ, µ) where σ : V → [0, 1] is a fuzzy subset V and µ : V × V → [0, 1] is a symmetric fuzzy relation on σ such that for all uv denotes the edge joining the vertices u and v. G * : (V, E) is called the underlying crisp graph of the fuzzy graph G : (σ, µ), where σ and µ are called membership function. Definition 2.2. Let G : (σ, µ) be a fuzzy graph. The degree of a vertex u is d G (u) = u =v µ(uv), for uv ∈ E and µ(uv) = 0, for uv not in E; this is equivalent to d G (u) = uv∈E µ(uv).