relation between wiener, szeged and detour indices
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abstract
in theoretical chemistry, molecular structure descriptors are used to compute properties of chemical compounds. among them wiener, szeged and detour indices play significant roles in anticipating chemical phenomena. in the present paper, we study these topological indices with respect to their difference number.
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Relation Between Wiener, Szeged and Detour Indices
In theoretical chemistry, molecular structure descriptors are used to compute properties of chemical compounds. Among them Wiener, Szeged and detour indices play significant roles in anticipating chemical phenomena. In the present paper, we study these topological indices with respect to their difference number.
full textDifferences between detour and Wiener indices
Let G be a connected graph and let μ(G) = DD(G) − W (G), where DD(G) and W (G) stand for the detour and Wiener numbers of G, respectively. Nadjafi-Arani et al. [Math. Comput. Model. 55 (2012), 1644– 1648] classified connected graphs whose difference between Szeged and Wiener numbers are n, for n = 4, 5. In this paper, we continue their work to prove that for any positive integer n = 1, 2, 4, 6 ...
full textRelationship between Edge Szeged and Edge Wiener Indices of Graphs
Let G be a connected graph and ξ(G) = Sze(G)−We(G), where We(G) denotes the edge Wiener index and Sze(G) denotes the edge Szeged index of G. In an earlier paper, it is proved that if T is a tree then Sze(T ) = We(T ). In this paper, we continue our work to prove that for every connected graph G, Sze(G) ≥ We(G) with equality if and only if G is a tree. We also classify all graphs with ξ(G) ≤ 5. ...
full textOn a Relation between Szeged and Wiener Indices of Bipartite Graphs
Hansen et. al., using the AutoGraphiX software package, conjectured that the Szeged index Sz(G) and the Wiener index W (G) of a connected bipartite graph G with n ≥ 4 vertices and m ≥ n edges, obeys the relation Sz(G) − W (G) ≥ 4n − 8. Moreover, this bound would be the best possible. This paper offers a proof to this conjecture.
full texton a relation between szeged and wiener indices of bipartite graphs
hansen et. al., using the autographix software package, conjectured that the szeged index $sz(g)$ and the wiener index $w(g)$ of a connected bipartite graph $g$ with $n geq 4$ vertices and $m geq n$ edges, obeys the relation $sz(g)-w(g) geq 4n-8$. moreover, this bound would be the best possible. this paper offers a proof to this conjecture.
full textThe Wiener, Szeged, and PI Indices of a Dendrimer Nanosta
Let G= V E be a simple connected graph. The distance between two vertices of G is defined to be the length of the shortest path between the two vertices. There are topological indices assigned to G and based on the distance function which are invariant under the action of the automorphism group of G. Some important indices assigned to G are the Wiener, Szeged, and PI index which we will find th...
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Journal title:
iranian journal of mathematical chemistryPublisher: university of kashan
ISSN 2228-6489
volume 5
issue Supplement 1 2014
Keywords
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