Roman domination is a historically inspired variety of general domination such that every vertex is labeled with labels from {0, 1, 2}. Roman domination number is the smallest of the sums of labels fulfilling condition that every vertex, labeled 0, has a neighbor, labeled 2. Using algebraic approach we give O(C) time algorithm for computing Roman domination number of special classes of polygrap...

Let nand k be positive integers and let G be a graph. A set D of vertices of G is defined to be an (n, k )-dominating set of G if every vertex of V( G) D is within distance n from at least k vertices of D. The minimum cardinality among all (n, k )-dominating sets of G is called the (n, k )-domination number of G and is denoted by 'Yn,k(G). A set I of vertices of G is defined to be an (n, k)inde...

In this paper, we evaluate the connected domination number of (Zn), in some case of n. We find out that the connected domination number of (Z p e1 1 ×p e2 2 ×···×p ek k ) is equal to k. Finally, we characterize the graphs in which γ ( (Zn)) = γc( (Zn)). AMS subject classification: 05C25, 05C69.