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Title: The Wiener, Eccentric Connectivity and Zagreb Indices of the Hierarchical Product of Graphs
Authors: Hossein-Zadeh, S.
Hamzeh, A.
Ashrafi, A.
Keywords: Wiener Index
Eccentric Connectivity Index
First Zagreb Index
First Zagreb Co-index
Issue Date: 2012
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Journal of Computing, Vol. 6, No 4, (2012), 409p-418p
Abstract: 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.
ISSN: 1312-6555
Appears in Collections:Volume 6 Number 4

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