On the sum of two parameters concerning independence and irredundance in a graph (Q1095940)

Let i(G) and IR(G) be the independent domination number and upper irredundance number of a graph G respectively. A conjecture that \(i(G)+IR(G)\leq 2p+2k-2\sqrt{2pk}\) was proposed in the paper of \textit{E. Cockayne, O. Favaron, C. Payan} and \textit{A. G. Thomason} in Discrete Math. 33, 249-258 (1981; Zbl 0471.05051), where \(p=| G|\) and k is the minimum degree of G. In this paper, we prove this conjecture.