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

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  • Submited: August 17, 2018
  • Published: August 17, 2018

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.

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.

How to Cite
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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How to Cite
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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