On the Distance Spectrum and Distance-Based Topological Indices of Central Vertex-Edge Join of Three Graphs - Haritha, T.; Chithra, A.V. (Armenian Journal of Mathematics, 2023)
In this paper, we introduce a new graph operation based on a central graph called central vertex-edge join (denoted by G_n_1^C (G_n_2^VG_n_3^E)) and then determine the distance spectrum of G_n_1^C (G_n_2^VG_n_3^E) in terms of the adjacency spectra of regular graphs G_1, G_2 and G_3 when G_1 is triangle-free. As a consequence of this result, we construct new families of non-D-cospectral D-equienergetic graphs. Moreover, we determine bounds for the distance spectral radius and distance energy of the central vertex-edge join of three regular graphs. In addition, we provide its results related to graph invariants like eccentric-connectivity index, connective eccentricity index, total-eccentricity index, average eccentricity index, Zagreb eccentricity indices, eccentric geometric-arithmetic index, eccentric atom-bond connectivity index, Wiener index. Using these results, we calculate the topological indices of the organic compounds Methylcyclobutane (C_5H_10) and Spirohexane (C_6H_10).