Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2013-10-01

Journal: ARS COMBINATORIA

Included Journals: Scopus、SCIE

Volume: 112

Page Number: 479-492

ISSN: 0381-7032

Key Words: Roman domination number; Generalized Petersen Graph

Abstract: A Roman domination function on a graph G = (V, E) is a function f: V (G) -> {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. The weight of a Roman domination function f is the value f (V (G)) = Sigma(u is an element of 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 (gamma R)(G). In this paper, we study the Roman domination number of generalized Petersen graphs P(n, 2) and prove that (gamma R)(P(n, 2)) = inverted right perpendicular8m/7inverted left perpendicular (n >= 5).