On Paired Double Domination number for Degree Splitting Graphs of Path and Cycle related Graphs
Keywords:
Double domination number, Paired - double domination number, Locating paired - double domination number.Abstract
In this paper, we introduced the new concept Paired double domination number for degree splitting graph of special graphs. A paired – double dominating set of a graph G with no isolated vertex is a double dominating sets of vertices whose induced subgraph has a perfect matching. A Paired double domination number γ_prdd (G) is the minimum cardinality of a paired double dominating set of G. Let G=(V,E) be a graph with V(G)=S_1∪S_2∪…∪S_t∪T, where S_i is the set having at least two vertices of same degree and T=V(G)- ∪S_i,where 1≤i≤t. The degree splitting graph DS(G) is obtained from G by adding vertices w_1,w_2,… w_tand joining w_i to each vertex of S_i for i=1,2,…t .We establish Paired double domination number for degree splitting graphs of path and cycle related graphs.
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