Independent and Total Domination in Antiprism Graphs from Convex Polytope

Let G = (V,E) be a connected graph. Antiprism graphs, defined as the skeletons of antiprism-shaped convex polytopes, consist of 2n vertices and 4n edges for an n-sided base. These graphs arise from convex polytopes, which are geometric structures formed as the convex hulls of finite point sets in Euclidean space ℝ d , preserving adjacency and incidence relations among vertices. Domination parameters such as the domination number γ(G), independent domination number γi(G), and total domination number γt(G) provide valuable insights into the structural properties and complexity of such graphs. In this paper, we focus on two classes of graphs derived from convex polytopes, denoted by R n and D n . We determine explicit formulas for the independent domination number and the total domination number of these graph families. Furthermore, we characterize optimal dominating sets and establish precise relationships between the geometric structure of antiprism-based graphs and their domination parameters. These findings extend existing domination theory to convex polytope graphs and highlight the theoretical significance of the interplay between discrete geometry and graph-theoretic domination properties.