The hyper-Wiener index of the generalized hierarchical product of graphs (original) (raw)

2011

a b s t r a c t Eliasi and Taeri [Extension of the Wiener index and Wiener polynomial, Appl. Math. Lett. 21 (2008) 916-921] introduced the notion of y-Wiener index of graphs as a generalization of the classical Wiener index and hyper Wiener index of graphs. They obtained some mathematical properties of this new defined topological index. In this paper, the join, Cartesian product, composition, disjunction and symmetric difference of graphs under y-Wiener index are computed. By these results most parts of a paper by Sagan et al. [The Wiener polynomial of a graph, Int. J. Quant. Chem. 60 (1996) 959-969] and another paper by Khalifeh et al. [The hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (2008) 1402-1407] are generalized.

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

Let G 1 = (V 1 , E 1 ) and G 2 = (V 2 , E 2 ) be two graphs having a distinguished or root vertex, labeled 0. The hierarchical product G 2 ⊓ G 1 of G 2 and G 1 is a graph with vertex set V 2 × V 1 . Two vertices y 2 y 1 and x 2 x 1 are adjacent if and only if y 1 x 1 ∈ E 1 and y 2 = x 2 ; or y 2 x 2 ∈ E 2 and y 1 = x 1 = 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.

Y-Wiener index of composite graphs

2011

The cut method on hypergraphs for the Wiener index

Journal of Mathematical Chemistry

The cut method has been proved to be extremely useful in chemical graph theory. In this paper the cut method is extended to hypergraphs. More precisely, the method is developed for the Wiener index of k-uniform partial cube-hypergraphs. The method is applied to cube-hypergraphs and hypertrees. Extensions of the method to hypergraphs arising in chemistry which are not necessary k-uniform and/or not necessary linear are also developed.

New composition of graphs and their Wiener Indices

In this paper, we define new graph operations F-composition F(G)[H], where F(G) be one of the symbols S(G), M(G), Q(G), T (G), Λ(G), Λ[G], D 2 (G), D 2 [G]. Further, we give some results for the Wiener indices of the these graph operations.

Wiener Index of Total Graph of Some Graphs Research

2017

Let G = (V,E) be a graph. The total graph T (G) of G is that graph whose vertex set is V ∪ E, and two vertices are adjacent if and only if they are adjacent or incident in G. For a graph G = (V,E), the graph G.Sm is obtained by identifying each vertex of G by a root vertex of Sm and the graph Sm.G is obtained by identifying each vertex of Sm except root vertex by any vertex of G, where Sm is a star graph with m vertices. In this paper, we consider G as the cycle graph Cn with n vertices and investigate the Wiener index of the total graphs of Cn.Sm and Sn.Cm. MSC: 05C12, 05C76

A New Approach to Compute Wiener Index

Journal of Computational and Theoretical Nanoscience, 2013

Distance properties of molecular graphs form an important topic in chemical graph theory. The Wiener index of a graph G is defined as the sum of all distances between distinct vertices of G. A lot of research has been devoted to finding Wiener index by brute force method. In this paper we develop a method to compute the Wiener index of certain chemical graphs without using distance matrix.

Peripheral Wiener Index of Graph Operations

2019

Peripheral Wiener index of a graph is the sum of the distance of the peripheral vertices of a graph. In this paper the peripheral Wiener index of graph operations is investigated.

The hyper-Wiener index of the generalized hierarchical product of graphs (original) (raw)

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