Advances and Applications in Discrete Mathematics
Volume 12, Issue 1, Pages 39 - 54
(July 2013)
|
|
COMPLEMENTARY TRIPLE CONNECTED DOMINATION NUMBER OF A GRAPH
G. Mahadevan, Selvam Avadayappan, J. Paulraj Joseph, B. Ayisha and T. Subramanian
|
Abstract: The concept of triple connected graphs with real life application was introduced in [7] by considering the existence of a path containing any three vertices of G. In [5], the authors introduced triple connected domination number of a graph. A subset S of V of a nontrivial graph G is said to be triple connected dominating set, if S is a dominating set and the induced subgraph is triple connected. The minimum cardinality taken over all triple connected dominating sets is called the triple connected domination number of G and is denoted by In this paper, we introduce a new domination parameter, called complementary triple connected domination number of a graph. A subset S of V of a nontrivial connected graph G is said to be complementary triple connected dominating set, if S is a dominating set and the induced subgraph is triple connected. The minimum cardinality taken over all complementary triple connected dominating sets is called the complementary triple connected domination number of G and is denoted by We determine this number for some standard classes of graphs and obtain bounds for general graphs. Its relationship with other graph theoretical parameters is also investigated. |
Keywords and phrases: domination number, triple connected graph, complementary triple connected domination number. |
|
Number of Downloads: 264 | Number of Views: 1053 |
|