Characterization of Bipartite Graphs with givenϒ2 (G)

Author: Zaw Myint

Abstract:

        In this paper, we first give a characterization of the bipartite graphs G satisfying ϒ2 (G)=3β(G)/2. Moreover, we compare the value of 2-domination number and independence number in trees and give bounds on these two parameters in terms of the order and the number of pendant vertices of the tree. More precisely we show that for a nontrivial T, β(T)≤ ϒ2 (T) ≤ 3β(T)/2, (n(T)+ℓ(T)+2/3≤ ϒ2 (T)≤(n(T)+ ℓ(T)/2 and β(T)≤(n(T)+ ℓ(T)-1)/2. Finally, characterize the trees achieving equality in each bound.

Published:  Myingyan Degree College Research Journal ( Vol-3 )