Volume :8 , Issue :2 ,Page : 82-91

Abstract :A b-coloring of a graph G by k colors is a proper vertex coloring such that in each color class, there exists a vertex adjacent to at least one vertex in every other color class and the b-chromatic number
b (G) of G is the largest integer k such that there is a b-coloring. A graph G is b-continuous if G has a b-coloring by k colors for every integer k satisfying
(G) ≤ k ≤
b (G). The b-spectrum S b (G) of G is the set of all integers k for which G has a b-coloring by k colors. The graph T(m, n) is the graph obtained by joining any vertex of cycle C m to a pendant vertex of path P n by an edge. In this paper, we find the b-chromatic number of square of Tadpole graphs. Also, b-continuity properties of these graphs are discussed.