TY - JOUR AU - K.M Dharmalingam, P.Nithya, PY - 2018/08/17 Y2 - 2024/03/28 TI - Color class domination and chromatic polynomial for ir-coloring and ND-coloring in fuzzy graphs JF - Asian Journal of Current Engineering and Maths JA - engineering and maths VL - 7 IS - 7 SE - Mathematics DO - UR - http://innovativejournal.in/index.php/ajcem/article/view/2272 SP - AB - <p>Let G be a fuzzy graph. A family &nbsp;of fuzzy sets on a set V is called k-fuzzy coloring of &nbsp;if i) &nbsp;ii) &nbsp;iii) for every strong edge &nbsp;(that is ., &nbsp;) of G, &nbsp; . 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.</p> ER -