A linear Vizing‐like relation relating the size and total domination number of a graph

We prove that m ≤ Δ (n ? γ_t) for every graph each component of which has order at least 3 of order n, size m, total domination number γ_t, and maximum degree Δ ≥ 3. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 285–290, 2005