Bhat, R.S.Sowmya, Kamath S.Surekha2020-03-302020-03-302013Lecture Notes in Engineering and Computer Science, 2013, Vol.1 LNECS, , pp.208-210https://idr.nitk.ac.in/jspui/handle/123456789/7305A vertex v in a graph G=(V,X) is said to be weak if d(v)?d(u) for every u adjacent to v in G. A set S ? V is said to be weak if every vertex in S is a weak vertex in G. A weak set which is independent is called a weak independent set (WIS). The weak independence number w?0(G) is the maximum cardinality of a WIS. We proved that w?0(G)? p-?. This bound is further refined in this paper and we characterize the graphs for which the new bound is attained.Book chapter