LAUSR

A vertex set S of a simple finite graph $$G=(V;E)$$G=(V;E) is said to be an independent set if there is no edge between any pair of vertices of S and a dominating set if for any $$v\in V-S$$v∈V-S, $$uv\in E$$uv∈E for some $$u\in S$$u∈S. If S is both independent and dominating in G, then S is an independent dominating set. Let i(G) denote the cardinality of a minimum independent dominating set of G. Set $$b_i(G)=\min \{|E'|~: E'\subseteq E, i(G)