A Note On Distance Graphs

Given a connected \((p, q)\) graph \(G\) with a number of central vertices, we form a new graph \(G^*\) as follows:

– **Vertex Set**: \(V(G^*) = V(G)\).
– **Edge Set**: Delete all the edges of \(G\). Introduce an edge between every central vertex and each non-central vertex of \(G\). Allow every pair of central vertices to be adjacent.

In this paper, we probed \(G^*\) and deduced a number of results.