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.

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In this paper, we introduce the eccentric harmonic index H e ¼ H e ðGÞ of a graph G, so that it is the sum of the terms 2 eiþej for the edges v i v j , where e i is the eccentricity of the i th vertex of the graph G. We compute the exact values of H e for some standard graphs. Bounds for H e are established. Relationships between H e and the eccentric connectivity index n c ðGÞ are derived.

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