Regular Fuzzy Graphs with Chromatic Numbers

Let G = (σ, µ) be a fuzzy graph on G∗ = (V, E). If each vertex in G has the same degree k, then G is said to be a vertex regular fuzzy graph or a k-vertex regular fuzzy graph. The minimum number of colors required to color all the vertices in such a way that no two adjacent vertices receive the same color is called the chromatic number and is denoted by χ(G). In this paper, we present results based on cubic graphs and their chromatic number with regular fuzzy graphs, which are briefly denoted by fr(G).