A note on independent domination in graphs of girth 5

Let G be a simple graph of order n, maximum degree ∆ and minimum degree δ ≥ 2. The independent domination number i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. The girth g(G) is the minimum length of a cycle in G. We establish sharp upper and lower bounds, as functions of n, ∆ and δ, for the independent domination number of graphs G with g(G) = 5.