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From Wiener Index to Molecules
Journal of Chemical Information and Modeling, 2005In this paper we present an algorithm for the generation of molecular graphs with a given value of the Wiener index. The high number of graphs for a given value of the Wiener index is reduced thanks to the application of a set of heuristics taking into account the structural characteristics of the molecules.
Gonzalo, Cerruela García +4 more
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Wiener Index of Hexagonal Systems
Acta Applicandae Mathematica, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dobrynin, Andrey A. +3 more
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The Overall Hyper-Wiener Index
Journal of Mathematical Chemistry, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, X. H., Lin, J. J.
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Hyper-Wiener Index vs. Wiener Index. Two Highly Correlated Structure-Descriptors
Monatshefte für Chemie - Chemical Monthly, 2003The Wiener (W) and hyper-Wiener (WW) indices of alkanes are found to be highly correlated. Hence, these two structure-descriptors pertain to the very same structural features of the underlying molecules and one of them may be viewed as superfluous. For alkane isomers with n carbon atoms, WW is bounded from both above and below by linear functions of W.
Ivan Gutman, Boris Furtula
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On Wiener index and Wiener polarity index of some polyomino chains
Journal of Discrete Mathematical Sciences and Cryptography, 2019AbstractA graph invariant is a numerical value that depicts the structural properties of an entire graph.
Sarfraz Ahmad +5 more
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On the Relation between W ‘/W Index, Hyper-Wiener Index, and Wiener Number
Journal of Chemical Information and Computer Sciences, 1999It is shown analytically that the W'/W index, the hyper-Wiener index, and the Wiener number are closely related graph-theoretical invariants for acyclic structures. A general analytical expression for the hyper-Wiener index of a tree is derived too.
Lerš, Nella +2 more
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On Wiener and terminal Wiener index of graphs
International Journal of Biomathematics, 2015The Wiener index is a topological index defined as the sum of distances between all pairs of vertices in a graph. It was introduced as a structural descriptor for molecular graphs of alkanes, which are trees with vertex degrees of four at the most. The terminal Wiener index is defined as the sum of distances between all pairs of pendent vertices in a ...
Babujee, J. Baskar, Senbagamalar, J.
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WIENER INDEX AND TRACEABLE GRAPHS
Bulletin of the Australian Mathematical Society, 2012AbstractIn this short paper, we show that, with three exceptions, if the Wiener index of a connected graph of order $n$ is at most $(n+ 5)(n- 2)/ 2$, then it is traceable.
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Wuhan University Journal of Natural Sciences, 2004
Based on distance matrixW, the novel topological indexW F is defined by the matricesX, W, L, asW F=WXL. WhereX is a row matrix, which expresses the bonding characteristics between adjacent atoms;L is a column matrix expressing the characteristic of vertexes in molecules;W is a distance matrix, which expresses the ...
Huang Yun-ping +3 more
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Based on distance matrixW, the novel topological indexW F is defined by the matricesX, W, L, asW F=WXL. WhereX is a row matrix, which expresses the bonding characteristics between adjacent atoms;L is a column matrix expressing the characteristic of vertexes in molecules;W is a distance matrix, which expresses the ...
Huang Yun-ping +3 more
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Relation between hyper-Wiener and Wiener index
Chemical Physics Letters, 2002Abstract An identity between the hyper-Wiener index ( WW ) and the Wiener index ( W ) of a tree is deduced, showing that these two molecular-structure-descriptors are more intimately connected than earlier believed. Let T be a tree on n vertices and e be its edge.
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