Valency based descriptors of certain types of chemical trees

2019 ◽  
Author(s):  
K. Pattabiraman ◽  
T. Suganya
Keyword(s):  
Chemical Trees

scholarly journals The inverse Wiener polarity index problem for chemical trees

PLoS ONE ◽  
2018 ◽  
Vol 13 (5) ◽  
pp. e0197142 ◽  
Author(s):  
Zhibin Du ◽  
Akbar Ali
Keyword(s):  
Polarity Index ◽  
Index Problem ◽  
Chemical Trees

A Linear Algorithm for the Hyper-Wiener Index of Chemical Trees

2001 ◽  
Vol 41 (4) ◽  
pp. 958-963 ◽  
Author(s):  
Roberto Aringhieri ◽  
Pierre Hansen ◽  
Federico Malucelli
Keyword(s):  
Wiener Index ◽  
Linear Algorithm ◽  
Chemical Trees

A note on chemical trees with minimum Wiener polarity index

2018 ◽  
Vol 335 ◽  
pp. 231-236 ◽  
Author(s):  
Akbar Ali ◽  
Zhibin Du ◽  
Muhammad Ali
Keyword(s):  
Polarity Index ◽  
Chemical Trees

Extremal trees with respect to the Steiner Wiener index

2019 ◽  
Vol 11 (06) ◽  
pp. 1950067
Author(s):  
Jie Zhang ◽  
Guang-Jun Zhang ◽  
Hua Wang ◽  
Xiao-Dong Zhang
Keyword(s):  
Maximum Degree ◽  
Computational Analysis ◽  
Degree Sequence ◽  
Wiener Index ◽  
Extremal Problems ◽  
Difficult Problem ◽  
Computational Results ◽  
Number Of Leaves ◽  
Extremal Structure ◽  
Chemical Trees

The well-known Wiener index is defined as the sum of pairwise distances between vertices. Extremal problems with respect to it have been extensively studied for trees. A generalization of the Wiener index, called the Steiner Wiener index, takes the sum of minimum sizes of subgraphs that span [Formula: see text] given vertices over all possible choices of the [Formula: see text] vertices. We consider the extremal problems with respect to the Steiner Wiener index among trees of a given degree sequence. First, it is pointed out minimizing the Steiner Wiener index in general may be a difficult problem, although the extremal structure may very likely be the same as that for the regular Wiener index. We then consider the upper bound of the general Steiner Wiener index among trees of a given degree sequence and study the corresponding extremal trees. With these findings, some further discussion and computational analysis are presented for chemical trees. We also propose a conjecture based on the computational results. In addition, we identify the extremal trees that maximize the Steiner Wiener index among trees with a given maximum degree or number of leaves.

scholarly journals Extremal Chemical Trees

2002 ◽  
Vol 57 (1-2) ◽  
pp. 49-51
Author(s):  
Miranca Fischermann ◽  
Ivan Gutman ◽  
Arne Hoffmann ◽  
Dieter Rautenbach ◽  
Dušica Vidovića ◽  
...  
Keyword(s):  
Carbon Atom ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Wiener Index ◽  
Graph Representation ◽  
Hosoya Index ◽  
Saturated Hydrocarbons ◽  
Physico Chemical ◽  
Graph Energy ◽  
Chemical Trees

A variety of molecular-graph-based structure-descriptors were proposed, in particular the Wiener index W. the largest graph eigenvalue λ1, the connectivity index X, the graph energy E and the Hosoya index Z, capable of measuring the branching of the carbon-atom skeleton of organic compounds, and therefore suitable for describing several of their physico-chemical properties. We now determine the structure of the chemical trees (= the graph representation of acyclic saturated hydrocarbons) that are extremal with respect to W , λ1, E, and Z. whereas the analogous problem for X was solved earlier. Among chemical trees with 5. 6, 7, and 3k + 2 vertices, k = 2,3,..., one and the same tree has maximum λ1 and minimum W, E, Z. Among chemical trees with 3k and 3k +1 vertices, k = 3,4...., one tree has minimum 11 and maximum λ1 and another minimum E and Z .

On the second maximum Wiener polarity index of chemical trees of a fixed order

2021 ◽  
Author(s):  
Akbar Ali ◽  
Zhibin Du ◽  
Syeda Sifwa Zaineb ◽  
Tariq Alraqad
Keyword(s):  
Polarity Index ◽  
Fixed Order ◽  
Chemical Trees

Chemical trees enumeration algorithms

4OR ◽  
2003 ◽  
Vol 1 (1) ◽  
Author(s):  
Roberto Aringhieri ◽  
Pierre Hansen ◽  
Federico Malucelli
Keyword(s):  
Enumeration Algorithms ◽  
Chemical Trees

scholarly journals ON MAXIMAL ENERGY AND HOSOYA INDEX OF TREES WITHOUT PERFECT MATCHING

2009 ◽  
Vol 81 (1) ◽  
pp. 47-57 ◽  
Author(s):  
HONGBO HUA
Keyword(s):  
Maximal Element ◽  
Perfect Matching ◽  
Undirected Graph ◽  
Unique Element ◽  
Hosoya Index ◽  
Maximal Energy ◽  
Molecular Graphs ◽  
The Family ◽  
Appl Math ◽  
Chemical Trees

AbstractLet G be a simple undirected graph. The energy E(G) of G is the sum of the absolute values of the eigenvalues of the adjacent matrix of G, and the Hosoya index Z(G) of G is the total number of matchings in G. A tree is called a nonconjugated tree if it contains no perfect matching. Recently, Ou [‘Maximal Hosoya index and extremal acyclic molecular graphs without perfect matching’, Appl. Math. Lett.19 (2006), 652–656] determined the unique element which is maximal with respect to Z(G) among the family of nonconjugated n-vertex trees in the case of even n. In this paper, we provide a counterexample to Ou’s results. Then we determine the unique maximal element with respect to E(G) as well as Z(G) among the family of nonconjugated n-vertex trees for the case when n is even. As corollaries, we determine the maximal element with respect to E(G) as well as Z(G) among the family of nonconjugated chemical trees on n vertices, when n is even.

Ordering chemical trees by Wiener polarity index

2017 ◽  
Vol 313 ◽  
pp. 301-312 ◽  
Author(s):  
Ali Reza Ashrafi ◽  
Ali Ghalavand
Keyword(s):  
Polarity Index ◽  
Chemical Trees

scholarly journals Chemical trees minimizing energy and Hosoya index

2008 ◽  
Vol 46 (1) ◽  
pp. 214-230 ◽  
Author(s):  
Clemens Heuberger ◽  
Stephan G. Wagner
Keyword(s):  
Hosoya Index ◽  
Chemical Trees
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