Eccentric Harmonic Index for the Cartesian Product of Graphs. (19th December 2022) - Jebreen, Kamel; Aftab, Muhammad Haroon; Sowaity, M. I.; Sharada, B.; Naji, A. M.; Pavithra, M.
Abstract : Suppose ρ is a simple graph, then its eccentric harmonic index is defined as the sum of the terms 2 / e a + e b for the edges v a v b, where e a is the eccentricity of the a th vertex of the graph ρ . We symbolize the eccentric harmonic index (EHI) as H e = H e ρ . In this article, we determine H e for the Cartesian product (CP) of particularly chosen graphs. Lower bounds for H e of the CP of the two graphs are established. The formulas of EHI for the Hamming and Hypercube graphs are obtained. These obtained formulas can be used in QSAR and QSPR studies to get a better understanding of their applications in mathematical chemistry.