Results 31 to 40 of about 16,423 (156)
Hosoya and Harary Polynomials of TOX(n),RTOX(n),TSL(n) and RTSL(n)
Discrete Dynamics in Nature and Society, 2019 In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound.
Lian Chen +5 more
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Hosoya polynomial of zigzag polyhex nanotorus [PDF]
Journal of the Serbian Chemical Society, 2008 The Hosoya polynomial of a molecular graph G is defined as ... , where d(u,v) is the distance between vertices u and v. The first derivative of H(G,l) at l = 1 is equal to the Wiener index of G, defined as .... . The second derivative of .... at l = 1 is
MEHDI ELIASI, BIJAN TAERI
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Mathematical aspects of Wiener index
Ars Mathematica Contemporanea, 2016 The Wiener index (i.e., the total distance or the transmission number), defined as the sum of distances between all unordered pairs of vertices in a graph, is one of the most popular molecular descriptors. In this article we summarize some results, conjectures and problems on this molecular descriptor, with emphasis on works we were involved in.
Martin Knor +2 more
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On the Graovac-Pisanski index [PDF]
Kragujevac Journal of Science, 2017 The Graovac-Pisanski index (GP index) is an algebraic approach for generalizing the Wiener index. In this paper, we compute the difference between the Wiener and GP indices for an infinite family of polyhedral graphs.
Hakimi-Nezhaad Mardjan +1 more
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On the Wiener Index of Orientations of Graphs
Discrete Applied Mathematics, 2022 The Wiener index of a strong digraph $D$ is defined as the sum of the distances between all ordered pairs of vertices. This definition has been extended to digraphs that are not necessarily strong by defining the distance from a vertex $a$ to a vertex $b$ as $0$ if there is no path from $a$ to $b$ in $D$.
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On the Wiener Polarity Index of Lattice Networks. [PDF]
PLoS ONE, 2016 Network structures are everywhere, including but not limited to applications in biological, physical and social sciences, information technology, and optimization. Network robustness is of crucial importance in all such applications.
Lin Chen +4 more
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The Wiener Index of Random Trees [PDF]
Combinatorics, Probability and Computing, 2002 The Wiener index is analysed for random recursive trees and random binary search trees in uniform probabilistic models. We obtain expectations, asymptotics for the variances, and limit laws for this parameter. The limit distributions are characterized as the projections of bivariate measures that satisfy certain fixed point equations.
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Journal of Chemistry, 2019 In this paper, with respect to the Wiener index, hyper-Wiener index, and Harary index, it gives some sufficient conditions for some graphs to be traceable, Hamiltonian, Hamilton-connected, or traceable for every vertex.
Guisheng Jiang, Lifang Ren, Guidong Yu
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On the Wiener index and the hyper-Wiener index of the Kragujevac trees
Proyecciones (Antofagasta), 2023 In this paper, the Wiener index and the hyper-Wiener index of the Kragujevac trees is computed in term of its vertex degrees. As application, we obtain an upper bond and a lower bound for the Wiener index and the hyper-Wiener index of these trees.
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Karpatsʹkì Matematičnì Publìkacìï, 2019 For a (molecular) graph, the Wiener index, hyper-Wiener index and degree distance index are defined as $$W(G)= \sum_{\{u,v\}\subseteq V(G)}d_G(u,v),$$ $$WW(G)=W(G)+\sum_{\{u,v\}\subseteq V(G)} d_{G}(u,v)^2,$$ and $$DD(G)=\sum_{\{u,v\}\subseteq V(G)}d_G(u,
N. Dehgardi +2 more
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