Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 4 2026 12 01 A note on independent domination in almost-regular graphs 1175 1180 15132 10.22049/cco.2026.31146.2756 EN Wayne Goddard School of Mathematical and Statistical Sciences, Clemson University, Clemson, USA Department of Mathematics and Applied Mathematics, University of Johannesburg Auckland Park, 2006 South Africa Michael A. Henning Department of Mathematics and Applied Mathematics, University of Johannesburg Auckland Park, 2006 South Africa Journal Article 2025 10 24 A classic result in domination theory is that a regular graph has independent domination number at most half the order. We strengthen this result to ``almost-regular'' graphs by showing that if a graph has minimum degree $\delta > 0$ and maximum degree at most $\delta + 3$, and the subgraph induced by the vertices of degree $\delta + 3$ (if any) is bipartite, then the independent domination number is at most half the order. We also discuss related questions. https://comb-opt.azaruniv.ac.ir/article_15132_c76ef09a70b3aba61b01d8a53b8439c4.pdf