Edge Roman Star Domination Number on Graphs Angshu Kumar Sinha, Akul Rana and Anita Pal Department of Mathematics, NSHM Knowledge Campus Durgapur -713212, INDIA. e-mail: [email protected] Department of Mathematics, Narajole Raj College Narajole, Paschim Medinipur721211, INDIA. e-mail: [email protected] Department of Mathematics, National Institute of Technology Durgapur Durgapur-713209, I...

The existence of a constant time algorithm for solving different domination problems on the subclass of polygraphs, rotagraphs and fasciagraphs, is shown by means of path algebras. As these graphs include products (the Cartesian, strong, direct, lexicographic) of paths and cycles, we implement the algorithm to get formulas in the case of the domination numbers, the Roman domination numbers and ...

For a graph G = (V,E), a Roman dominating function on G is a function f : V (G) → {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman dominating function is the value f(V (G)) = ∑ u∈V (G) f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G, denoted by γR (G). T...