Exploring the Structural Analysis of the Vectors Connectivity of Josephus Cube Interconnection Network: A Graph Theoretic Approach

Abstract

In this paper, we studied the structural analysis of vectors of the Josephus Cube interconnection network. We explored the representation and properties of the graph model of the Josephus Cube and studied the relationship between the connectivity of nodes (processors). In this study, we have also presented the vertex-to-vertex and edge-to-edge connectivity matrix of the Josephus Cube using bitwise binary complements of the vector to find the complement of degree 4. We found the tautology between complements of different sets of nodes and chordal ring edge sets of the Josephus Cube.