Displaying similar documents to “The Wiener polynomial of the k th power graph.”

The Eccentric Connectivity Polynomial of some Graph Operations

Ashrafi, A., Ghorbani, M., Hossein-Zadeh, M. (2011)

Serdica Journal of Computing

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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. ...

Degree polynomial for vertices in a graph and its behavior under graph operations

Reza Jafarpour-Golzari (2022)

Commentationes Mathematicae Universitatis Carolinae

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We introduce a new concept namely the degree polynomial for the vertices of a simple graph. This notion leads to a concept, namely, the degree polynomial sequence which is stronger than the concept of degree sequence. After obtaining the degree polynomial sequence for some well-known graphs, we prove a theorem which gives a necessary condition for the realizability of a sequence of polynomials with positive integer coefficients. Also we calculate the degree polynomial for the vertices...

The Wiener, Eccentric Connectivity and Zagreb Indices of the Hierarchical Product of Graphs

Hossein-Zadeh, S., Hamzeh, A., Ashrafi, A. (2012)

Serdica Journal of Computing

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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...