Geodesic
The Wiener, Eccentric Connectivity and Zagreb Indices of the Hierarchical Product of Graphs
Serdica Journal of Computing, Tome 6 (2012) no. 4, pp. 409-418.

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Let G1 = (V1, E1) and G2 = (V2, E2) be two graphs having a distinguished or root vertex, labeled 0. The hierarchical product G2 ⊓ G1 of G2 and G1 is a graph with vertex set V2 × V1. Two vertices y2y1 and x2x1 are adjacent if and only if y1x1 ∈ E1 and y2 = x2; or y2x2 ∈ E2 and y1 = x1 = 0. In this paper, the Wiener, eccentric connectivity and Zagreb indices of this new operation of graphs are computed. As an application, these topological indices for a class of alkanes are computed. ACM Computing Classification System (1998): G.2.2, G.2.3.
Keywords: Wiener Index, Eccentric Connectivity Index, First Zagreb Index, First Zagreb Co-index 
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Hossein-Zadeh, S.; Hamzeh, A.; Ashrafi, A. The Wiener, Eccentric Connectivity and Zagreb Indices of the Hierarchical Product of Graphs. Serdica Journal of Computing, Tome 6 (2012) no. 4, pp. 409-418. http://geodesic.mathdoc.fr/item/SJC_2012_6_4_a3/