Given a graph (Figure presented.), a dominating set of (Figure presented.) is a set (Figure presented.) of vertices such that each vertex not in (Figure presented.) has a neighbor in (Figure presented.). Let (Figure presented.) denote the minimum size of a dominating set of (Figure presented.). The independent domination number of (Figure presented.), denoted (Figure presented.), is the minimum size of a dominating set of (Figure presented.) that is also independent. We prove that if (Figure presented.) is a cubic graph without 4-cycles, then (Figure presented.), and the bound is tight. This result improves upon two results from two papers by Abrishami and Henning. Our result also implies that every cubic graph (Figure presented.) without 4-cycles satisfies (Figure presented.), which supports a question asked by O and West.
We thank the referees for their careful reading and helpful comments that improved the readability of the paper. Eun\u2010Kyung Cho was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF\u20102020R1I1A1A01058587). Ilkyoo Choi was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF\u20102018R1D1A1B07043049), and also by the Hankuk University of Foreign Studies Research Fund. Boram Park was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF\u20102022R1F1A1069500).
