The energy of a vertex vᵢ in a graph G is defined as EG (vᵢ) = |A|₈₈, where A is the adjacency matrix of G, A^* denotes the conjugate transpose of A, and |A| = (AA^*) ^1/2. The total energy of the graph, E (G), is then the sum of the energies of all vertices: E (G) = EG (v₁) + EG (v₂) + + EG (vₙ). In this paper, we compute the vertex energy for several well-known regular graphs, including the Frucht graph, Desargues graph, Tutte-Coxeter graph, Heawood graph, Shrikhande graph, and Petersen graph.
Nagesh et al. (Sat,) studied this question.