Dominating Coloring Number of Claw-free Graphs

Dominator and total dominator colorings in vague graphs

“…Proposition 11. (see [28]) For any vague graph G with G ∼ = C n (n ≥ 3), we have χ d (G) = 3 for n ≡ 3 (mod 6) and…”

“…After that, they studied the bounds and realization of the dominator chromatic number in terms of chromatic number and domination number [26] and the dominator colorings in bipartite graphs [27]. Recently, several researchers have theoretically investigated the dominator coloring number of Claw-free graph [28], Certain Cartesian Products [29], trees [30] and more [31,32]. Motivated by dominator chromatic number, Kazemi [33] studied the new concept of a total dominator chromatic number of a graph.…”