PROMOTING ACCESS TO AFRICAN RESEARCH

Quaestiones Mathematicae

Log in or Register to get access to full text downloads.

Remember me or Register



DOWNLOAD FULL TEXT Open Access  DOWNLOAD FULL TEXT Subscription or Fee Access

Domination versus disjunctive domination in graphs

Michael A Henning, Sinclair A Marcon

Abstract


A dominating set in a graph G is a set S of vertices of G such that every vertex not in S is adjacent to a vertex of S. The domination number of G is the minimum cardinality of a dominating set of G. For a positive integer b, a set S of vertices in a graph G is a b-disjunctive dominating set in G if every vertex v not in S is adjacent to a vertex of S or has at least b vertices in S at distance 2 from it in G. The b-disjunctive domination number of G is the minimum cardinality of a b-disjunctive dominating set. In this paper, we continue the study of disjunctive domination in graphs. We present properties of b-disjunctive dominating sets in a graph. A characterization of minimal b-disjunctive dominating sets is given. We obtain bounds on the ratio of the domination number and the b-disjunctive domination number for various families of graphs, including regular graphs and trees.




http://dx.doi.org/10.2989/16073606.2015.1068237
AJOL African Journals Online