Connection graphs for 3-triangulations of toroids
Nada Mladenovic, Milica Stojanović · Filomat · 2024
Itis known that all convex polytopes admit a triangulation without additional vertices, however this does not hold in general for non-convex polyhedra. If 3-triangulation of some polyhedron is possible, then a connection graph is introduced in such a way that convex pieces of that polyhedron are represented by graph nodes. A method for constructing a polyhedron P based on a given connected undirected graph is given and the properties of P are investigated. The algorithms for computing the numbers of vertices, edges, faces and handles of P are also given.