In this study, we exclusively focus on simple finite undirected graphs. A simple undirected graph is represented as G = (V, E), where E ⊆ V × V is a set ensuring that (v, v) / ∈ E for all v ∈ V , and if (v, u) ∈ E, then (u, v) ∈ E. Here, V signifies the vertex set and E represents the edge set. In a graph G, two vertices u and v are considered adjacent, or neighbors, if (u, v) forms an edge in G, denoted as u ∼ v. If all the vertices of G are pairwise adjacent, then G is complete. A complete graph on n vertices is denotaded as K n . The degree (or valency) d v of a vertex v is the number of edges at v; this is equal to the number of neighbours of v. The number δ(G)