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A k -class domination coloring (k -cd-coloring) is a partition of the vertex set of a graph G into k independent sets V 1 , ... , V k , where each V i is dominated by some vertex u i of G. The least integer k such that G admits a k -cd-coloring is called the cd-chromatic number, χ c d (G) , of G. A subset S of the vertex set of a graph G is called a subclique in G if d G (x , y) ≠ 2 for every x , y ∈ S. The cardinality of a maximum subclique in G is called the subclique number, ω s (G) , of G. In this paper, we present algorithms to compute an optimal cd-coloring and a maximum subclique of (i) trees with time complexity O (n) and (ii) co-bipartite graphs with time complexity O (n 2. 5). This improves O (n 3) algorithms by Shalu et al. (2017, 2020). In addition, we prove tight upper bounds for the subclique number of the class of (i) P 5 -free graphs and (ii) double-split graphs. [ABSTRACT FROM AUTHOR]