A CORRECTION TO A PAPER ON ROMAN κ-DOMINATION IN GRAPHS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 50, Issue 2, 2013, pp.469-473
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2013.50.2.469

Title & Authors

A CORRECTION TO A PAPER ON ROMAN κ-DOMINATION IN GRAPHS

Mojdeh, Doost Ali; Moghaddam, Seyed Mehdi Hosseini;

Mojdeh, Doost Ali; Moghaddam, Seyed Mehdi Hosseini;

Abstract

Let G = (V, E) be a graph and k be a positive integer. A -dominating set of G is a subset such that each vertex in has at least neighbors in S. A Roman -dominating function on G is a function : V {0, 1, 2} such that every vertex with = 0 is adjacent to at least vertices , , , with = 2 for = 1, 2, , . In the paper titled "Roman -domination in graphs" (J. Korean Math. Soc. 46 (2009), no. 6, 1309-1318) K. Kammerling and L. Volkmann showed that for any graph G with vertices, min , and the equality holds if and only if or and or and G or has a vertex of degree - 1 and its complement has a vertex of degree - 2. In this paper we find a counterexample of Kammerling and Volkmann's result and then give a correction to the result.

Keywords

dominating set;Roman k-dominating function;correction;

Language

English

References

1.

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

2.

K. Kammerling and L. Volkmann, Roman k-domination in graphs, J. Korean Math. Soc. 46 (2009), no. 6, 1309-1318.

3.

C. S. Liao and G. J. Chang, Algorithmic aspect of k-tuple domination in graphs, Taiwanese J. Math. 6 (2002), no. 3, 415-420.