Results 161 to 170 of about 1,818 (187)

Hosoya polynomials of random benzenoid chains

2016
Summary: Let \(G\) be a molecular graph with vertex set \(V(G)\), \(d_G(u, v)\) the topological distance between vertices \(u\) and \(v\) in \(G\). The Hosoya polynomial \(H(G, x)\) of \(G\) is a polynomial \(\sum_{\{u, v\}\subseteq V(G)}x^{d_G(u, v)}\) in variable \(x\). In this paper, we obtain an explicit analytical expression for the expected value
Xu, S.-J., He, Q.-H., Zhou, S., Chan, W.
openaire   +2 more sources

Hosoya polynomials of armchair open‐ended nanotubes

International Journal of Quantum Chemistry, 2006
AbstractFor a connected graph G we denote by d(G,k) the number of vertex pairs at distance k. The Hosoya polynomial of G is H(G,x) = ∑k≥0 d(G,k)xk. In this paper, analytical formulae for calculating the polynomials of armchair open‐ended nanotubes are given. Furthermore, the Wiener index, derived from the first derivative of the Hosoya polynomial in x =
Shoujun Xu, Heping Zhang
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The Hosoya Polynomial of One-Heptagonal Nanocone

Current Nanoscience, 2013
For a molecular graph G with vertex set V (G) , we denote by dG (u,v ) the distance between vertices u and v in G ...
Shou-Jun Xu, Qiu-Xia Zhang
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The Hosoya Polynomial of One-Pentagonal Carbon Nanocone

Fullerenes, Nanotubes and Carbon Nanostructures, 2014
Let G be a chemical graph with vertex set V(G) and the distance between vertices u and v in G. The Hosoya polynomial in variable x of graph G is . In this article, we give an analytical expression for calculating the Hosoya polynomial of one-pentagonal carbon nanocone. Furthermore, a series of distance-based molecular structure descriptors, such as the
Qiu-Xia Zhang, Shou-Jun Xu, Hai-Yang Chen   +2 more
openaire   +1 more source

Hosoya polynomial and Wiener index of concatenated octachains

2020
Summary: Wiener index of a connected graph \(G=(V,E)\) is defined as \(W(G)=\sum_{\{u,v\}\subset V(G)}d(u,v)\) and Hosoya polynomial is defined as \(H(G,x)=\sum_{\{u,v\}\subset V(G)}x^{d(u,v)}\). In this paper, Wiener index and Hosoya polynomials of several types of graphs consisting of concatenated octagon rings which are used in chemistry ...
Cangül, İsmail Naci, Amudha, B B, Srınıvasa, Rao   +2 more
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Hosoya Polynomial of an Infinite Family of Dendrimer Nanostar

2011
Let G be a simple graph. The Hosoya polynomial of G is ( , ) , ( , ) = { , } ( ) xd u v H G x  u v V G where d(u,v) denotes the distance between vertices u and v . The dendrimer nanostar is a part of a new group of macromolecules. In this paper we compute the Hosoya polynomial for an infinite family of dendrimer nanostar.
ESLAHCHI, CH., ALIKHANI, S., AKHBARI, M.
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Exceptional points in lossy media lead to deep polynomial wave penetration with spatially uniform power loss

Nature Nanotechnology, 2022
Alexander Yulaev, Sangsik Kim, Qing Li
exaly  

Simple Local Polynomial Density Estimators

Journal of the American Statistical Association, 2020
Matias D Cattaneo, Michael Jansson
exaly  

A Polynomial Kernel Induced Distance Metric to Improve Deep Transfer Learning for Fault Diagnosis of Machines

IEEE Transactions on Industrial Electronics, 2020
Bin Yang, Yaguo Lei, Feng Jia
exaly  

The kernel polynomial method

Reviews of Modern Physics, 2006
Gerhard Wellein, Andreas Alvermann, Holger Fehske   +2 more
exaly