Signed Roman Domination Number of Generalized Petersen Graph
Abstract: A signed Roman Dominating Function (SRDF) on a graph G is a function f: V (G) {-1, 1, 2} such that _ (uN|V|) f (u) 1 for every v V (G) and every vertex u V (G) for which f (u) = -1 is adjacent to at least one vertex w for which f (w) = 2. The weight of SRDF is the sum of its function values over all vertices. The signed Roman domination number of G is the minimum weight of a SRDF in G. For natural number n and k, where n > 2k, a generalized Petersen graph P (n, k) is obtained by letting its vertex set to be {u1, u2, , un, v1, v2, , vn} and its edge set to be {ui ui+1, ui vi, vi vi+k}; where i = 1, 2,. . . , n and subscripts are reduced modulo n. In this paper we determine the signed Roman domination number of generalized Petersen graph P (n, k) for k = 1 & 3. We characterize generalized Petersen graph which have efficient signed Roman domination number.
Keywords: Generalized Petersen graph, Roman domination, Signed domination, signed Roman dominating function, signed Roman domination number & efficient signed Roman domination
How to Cite?: Shailaja S. Shirkol, Manjula C. Gudgeri, "Signed Roman Domination Number of Generalized Petersen Graph", Volume 3 Issue 12, December 2014, International Journal of Science and Research (IJSR), Pages: 2630-2633, https://www.ijsr.net/getabstract.php?paperid=SUB141066, DOI: https://dx.doi.org/10.21275/SUB141066