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

AbstractLet 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) ⩽ 2p + 2k − 2√22pk was proposed in [1], where p = |G| and k is the minimum degree of G. In this paper, we prove this conjecture