International Journal of Combinatorics
Volume 2012 (2012), Article ID 831489, 7 pages
Research Article

Graphs with Constant Sum of Domination and Inverse Domination Numbers

Department of Mathematics, Manonmaniam Sundaranar University, Tamil Nadu, Tirunelveli 627 012, India

Received 1 March 2012; Accepted 10 July 2012

Academic Editor: Martin Kochol

Copyright © 2012 T. Tamizh Chelvam and T. Asir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A subset D of the vertex set of a graph G, is a dominating set if every vertex in 𝑉 𝐷 is adjacent to at least one vertex in D. The domination number 𝛾 ( 𝐺 ) is the minimum cardinality of a dominating set of G. A subset of 𝑉 𝐷 , which is also a dominating set of G is called an inverse dominating set of G with respect to D. The inverse domination number 𝛾 ( 𝐺 ) is the minimum cardinality of the inverse dominating sets. Domke et al. (2004) characterized connected graphs G with 𝛾 ( 𝐺 ) + 𝛾 ( 𝐺 ) = 𝑛 , where n is the number of vertices in G. It is the purpose of this paper to give a complete characterization of graphs G with minimum degree at least two and 𝛾 ( 𝐺 ) + 𝛾 ( 𝐺 ) = 𝑛 1 .