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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...
The eccentric connectivity index of a graph G, ξ^C, was proposed
by Sharma, Goswami and Madan. It is defined as ξ^C(G) =
∑ u ∈ V(G) degG(u)εG(u), where degG(u) denotes the degree of the vertex x
in G and εG(u) = Max{d(u, x) | x ∈ V (G)}. The eccentric connectivity
polynomial is a polynomial version of this topological index. In this paper,
exact formulas for the eccentric connectivity polynomial of Cartesian
product, symmetric difference, disjunction and join of graphs are presented.
...
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