Bhat, R.S.Kamath, S.S.Surekha2026-02-062013Lecture Notes in Engineering and Computer Science, 2013, Vol.1 LNECS, , p. 208-21020780958https://doi.org/https://idr.nitk.ac.in/handle/123456789/32703A 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 wβ0(G) is the maximum cardinality of a WIS. We proved that wβ0(G)≤ p-δ. This bound is further refined in this paper and we characterize the graphs for which the new bound is attained.Weak degreeWeak dominationWeak independence number