Interconnection Networks via Adjacencies and Their Vertex-Degree Based Graph Invariants

Interconnection Networks are a boon to human made large computing systems which are often designed based on the need. In this paper, we address the question of obtaining an interconnection network to suit a specific need which is a cumbersome procedure. The methods for constructing infinitely large interconnection networks from any simple, undirected graph \(G\) is illustrated and their properties are discussed. Further, we study the behaviour of certain vertex-degree based graph invariants of the constructed networks under the transformations by means of graph operation and obtain explicit relations for energy and some degree-based topological indices. Also, we show that they can be computed in polynomial time for these constructed networks. By doing so, we also obtain new methods of constructing infinite families of integral graphs.