Color class domination and chromatic polynomial for ir-coloring and ND-coloring in fuzzy graphs

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K.M Dharmalingam, P. (2018). Color class domination and chromatic polynomial for ir-coloring and ND-coloring in fuzzy graphs. Asian Journal of Current Engineering and Maths, 7(7). Retrieved from http://innovativejournal.in/index.php/ajcem/article/view/2272
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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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