Graphs with Constant Sum of Domination and Inverse Domination Numbers. (27th August 2012)

• Record Type: Journal Article
• Authors: Tamizh Chelvam, T.; Asir, T.
• Other Names: Kochol Martin Academic Editor.
• Is Part Of: International journal of combinatorics. Volume 2012(2012)
• Publication Date: 2012-08-27
• Subjects: Combinatorial analysis -- Periodicals; Combinatorial analysis; Periodicals; Electronic journals; 511.605
• DOI: 10.1155/2012/831489
• Languages: English
• ISSNs: 1687-9163

Abstract

Abstract : 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 .