Independent Restrained k - Rainbow Dominating Function

M Esakki Dharani, A Nagarajan, K Palani


Let G be a graph and let f be a function that assigns to each vertex a set of colors chosen from the set {1, 2…, k} that is f: V(G)  P [1,2,…,k]. If for each vertex v  V(G) such that f(v) =  .we have  then f is called the k – Rainbow Dominating Function (KRDF) of G. A k – Rainbow Dominating Function is said to be Independent Restrained k - Rainbow Dominating function if (i)The set of vertices assigned with non – empty set is independent. (ii)The induced subgraph of G, by the vertices with label   has no isolated vertices. The weight w(f) of a function f is defined as w(f) =  .The Independent Restrained k – Rainbow Domination number is the minimum weight of G. In this paper we introduce Independent Restrained k – Rainbow Domination and find for some graphs


Independent, Restrained, Rainbow domination number, weight

Full Text:



J. Amjadi S.M. Sheikholeslami. L. Volkmann. Rainbow Restrained domination numbers in graphs, in Ars Combinatoria

B. Bresar,M.Henning,D.Rall, Rainbow domination in graphs, Taiwanese J.Math. 12 (2008), 213–225.

Fujita.S, Furuyana.M, Magnant C general bounds on rainbow domination numbers. Graphs Combin 2015,31, 601-613.

Hao, G.L, Quian,J.G. On the rainbow domination number of digraphs. Graphs Combin 2016, 32,1903 -1913.

T.W. Haynes, S.T.Hedetniemi and P.J. Slater, Fundamentals of Domination in graphs, Marcel Dekker, New York, 1998.

Hong Gao, Changqing Xi, Yuansheng Yang. The 3-rainbow domination number of the cartesian product of the cycles.

Shao z h, Liang M L,Yin C, Pavlic P, Zerovnik J. On rainbow domination number of graphs. Inform. Sci. 2014, 254,225-234.

Zehui Shao, Zepeng Li, Aljosa Peperko, Jiafu Wan. Independent rainbow domination of graphs.



  • There are currently no refbacks.

Copyright (c) 2022 M Esakki Dharani, A NAGARAJAN, K Palani

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.