Independent Domination and Minimum Maximal Matchings in Clique-Fiber Cartesian Products

Abstract

Version 1.0.0. This preprint studies the independent domination number i(G) and the minimum cardinality s(G) of a maximal matching in Cartesian products with complete-graph fibers. For every nonempty finite simple graph H of order h and every m ≥ 2, it proves the universal bound s(H □ Km) ≥ ⌈(m-1)h/2⌉. For odd m ≥ 3, equality is characterized by m-colourability of H. A sufficient equality condition is established for even m ≥ 4. The paper also determines both parameters for every cycle–clique product, including exact prism formulas and all equality cases in the comparison i ≤ s. This unified and substantially revised manuscript incorporates, reorganizes, and supersedes two preliminary Zenodo notes: 10.5281/zenodo.21817792 and 10.5281/zenodo.21819243. The degree-threshold identity used as background was previously recorded in arXiv:2608.07956 and is not claimed as a new result here. The deposit includes the manuscript PDF, a full source and verification archive, a minimal arXiv source archive, and SHA-256 checksums.