Vertex cover number in diverse graph architectures

Finding a minimum-sized set of vertices in a graph such that each edge in the graph is incident to at least one vertex in the set is the objective of the study of vertex cover problem. Mathematically, a vertex cover of a graph G is a set S of vertices in G such that every edge of G has at least one end vertex in S. The vertex covering number denoted by β(G) is the minimum cardinality taken over all vertex covering sets of G. In this paper, we obtain the vertex cover number of certain architectures such as hypertrees, glued trees, triangular graphs, and honeycomb rectangular torus.