A set S of vertices in a graph G is an independent dominating set of G if D is an independent set and every vertex not in D is adjacent to a vertex in D. Moreover, since any total co-independent dominating set is a total dominating set, we characterize all the trees having equal total co-independent domination number and total domination number. Proof — Let I be an independent dominating set of cardinality i G. Since I is independent, no two vertices of I are adjacent in G. Most users should sign in with their email address.
On locating independent domination number of amalgamation graphs
AIP Conference Proceedings, , ] Volume 3 Issue 4, — Issue 3, — Issue 2, — Issue 1, 1— Then at least two vertices, say, u , v in D , are adjacent to each other. We also study the relationship between independent [1; 2]-sets and independent dominating sets in this graph class, that allows us to obtain an upper bound for the associated parameter, the independent [1; 2]-number, in terms of the independent domination number. The authors in  listed over papers related to domination in graphs in over 75 variation.
On locating independent domination number of amalgamation graphs - IOPscience
Vasanthi and Subramanian [ 2 ] introduced vertex covering transversal domination in graphs using minimum vertex covering set in a graph. Link to Publisher's Edition http: Support Center Support Center. The converse is not true. You could not be signed in. Online access to the content of recent issues is by subscription, or purchase of single articles. Laskar, On domination and independent domination numbers of a graph, Discrete Mathematics, Vol.
It must have at least 2 vertices as it intersects both S 1 and S 2. We also investigate the degree equitable domination in the corona of graphs. Proof — Let D be a minimum dominating set which is not an independent set of G. Then S is a vertex covering transversal dominating set of G. Were these topics helpful?