Color class domination and chromatic polynomial for ir-coloring and ND-coloring in fuzzy graphs
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Abstract
Let G be a fuzzy graph. A family of fuzzy sets on a set V is called k-fuzzy coloring of if i) ii) iii) for every strong edge (that is ., ) of G, . The minimum number of k for which there exists a k-fuzzy coloring is called fuzzy chromatic number of G and is denoted by . Then is the partition of independent sets of vertices of G in which each sets has the same color is called the fuzzy chromatic partition. A fuzzy dominator coloring of a fuzzy graph G is a proper fuzzy coloring of G in which every vertex of G dominates every vertex of at least one color class. The minimum number of colors required for a fuzzy dominator coloring of G is called the fuzzy dominator chromatic number (FDCN) and is denoted by . In this chapter , we introduce a new class of color partition and their related concepts. Also, we extensively studied the concept of chromatic polynomial for irregular fuzzy coloring and fuzzy neighborhood distinguished coloring.
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