A Roman dominating function on a graph G = (V, E) is a function f : V â†’ {0, 1, 2} such that every vertex v âˆˆ V with f(v) = 0 has at least one neighbor u âˆˆ V with f(u) = 2. The weight of a Romanâ€¦ (More)

Let G = (V, E) be a graph and p be a positive integer. A subset S âŠ† V is called a p-dominating set if each vertex not in S has at least p neighbors in S. The p-domination number Î³p(G) is the size ofâ€¦ (More)

A Roman dominating function on a graph G = (V, E) is a function f : V â†’ {0, 1, 2} satisfying the condition that every vertex u with f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. Theâ€¦ (More)

Let G = (V , E) be a graph. A subset D âŠ† V is a dominating set if every vertex not in D is adjacent to a vertex in D. A dominating set D is called a total dominating set if every vertex in D isâ€¦ (More)

Let n and k be integers with n â‰¥ k â‰¥ 0. This paper presents a new class of graphs H(n, k), which contains hypercubes and some well-known graphs, such as Johnson graphs, Kneser graphs and Petersenâ€¦ (More)

Let and be two undirected nontrivial graphs. The Kronecker product of and denoted by with vertex set , two vertices and are adjacent if and only if and . This paper presents a formula for computingâ€¦ (More)

Let G be a graph without isolated vertices. The total domination number of G is the minimum number of vertices that can dominate all vertices in G, and the paired domination number of G is theâ€¦ (More)