On the Distance Spectrum and Distance-Based Topological Indices of Central Vertex-Edge Join of Three Graphs

T. Haritha; A.V. Chithra

doi:10.52737/18291163-2023.15.10-1-16

Authors

T. Haritha National Institute of Technology Calicut
A.V. Chithra National Institute of Technology Calicut

DOI:

https://doi.org/10.52737/18291163-2023.15.10-1-16

Keywords:

Distance Matrix, Distance Eigenvalues, Distance Equienergetic Graphs, Topological Indices

Abstract

In this paper, we introduce a new graph operation based on a central graph called central vertex-edge join (denoted by $G_{n_1}^C \triangleright (G_{n_2}^V\cup G_{n_3}^E)$) and then determine the distance spectrum of $G_{n_1}^C \triangleright (G_{n_2}^V\cup G_{n_3}^E)$ 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 $(C_6H_{10})$.

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