On acyclic molecular graphs with maximal Hosoya index, energy, and short diameter

2006 ◽  
Vol 43 (1) ◽  
pp. 328-337 ◽  
Author(s):  
Jianping Ou
Keyword(s):  
Hosoya Index ◽  
Molecular Graphs ◽  
Short Diameter

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.

scholarly journals The largest n - 1 Hosoya indices of unicyclic graphs

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2573-2581 ◽  
Author(s):  
Guihai Yu ◽  
Lihua Feng ◽  
Aleksandar Ilic
Keyword(s):  
Independent Sets ◽  
Hosoya Index ◽  
Unicyclic Graphs ◽  
Molecular Graphs ◽  
Appl Math

The Hosoya index Z(G) of a graph G is defined as the total number of edge independent sets of G. In this paper, we extend the research of [J. Ou, On extremal unicyclic molecular graphs with maximal Hosoya index, Discrete Appl. Math. 157 (2009) 391-397.] and [Y. Ye, X. Pan, H. Liu, Ordering unicyclic graphs with respect to Hosoya indices and Merrifield-Simmons indices, MATCH Commun. Math. Comput. Chem. 59 (2008) 191-202.] and order the largest n - 1 unicyclic graphs with respect to the Hosoya index.

Higher-Order and Mixed Discrete Derivatives such as a Novel Graph- Theoretical Invariant for Generating New Molecular Descriptors

2019 ◽  
Vol 19 (11) ◽  
pp. 944-956 ◽  
Author(s):  
Oscar Martínez-Santiago ◽  
Yovani Marrero-Ponce ◽  
Ricardo Vivas-Reyes ◽  
Mauricio E.O. Ugarriza ◽  
Elízabeth Hurtado-Rodríguez ◽  
...  
Keyword(s):  
Molecular Descriptors ◽  
3D Qsar ◽  
Higher Order ◽  
Molecular Structures ◽  
Qsar Modeling ◽  
Statistical Parameters ◽  
Molecular Graphs ◽  
New Family ◽  
Mixed Derivatives ◽  
Discrete Derivative

Background: Recently, some authors have defined new molecular descriptors (MDs) based on the use of the Graph Discrete Derivative, known as Graph Derivative Indices (GDI). This new approach about discrete derivatives over various elements from a graph takes as outset the formation of subgraphs. Previously, these definitions were extended into the chemical context (N-tuples) and interpreted in structural/physicalchemical terms as well as applied into the description of several endpoints, with good results. Objective: A generalization of GDIs using the definitions of Higher Order and Mixed Derivative for molecular graphs is proposed as a generalization of the previous works, allowing the generation of a new family of MDs. Methods: An extension of the previously defined GDIs is presented, and for this purpose, the concept of Higher Order Derivatives and Mixed Derivatives is introduced. These novel approaches to obtaining MDs based on the concepts of discrete derivatives (finite difference) of the molecular graphs use the elements of the hypermatrices conceived from 12 different ways (12 events) of fragmenting the molecular structures. The result of applying the higher order and mixed GDIs over any molecular structure allows finding Local Vertex Invariants (LOVIs) for atom-pairs, for atoms-pairs-pairs and so on. All new families of GDIs are implemented in a computational software denominated DIVATI (acronym for Discrete DeriVAtive Type Indices), a module of KeysFinder Framework in TOMOCOMD-CARDD system. Results: QSAR modeling of the biological activity (Log 1/K) of 31 steroids reveals that the GDIs obtained using the higher order and mixed GDIs approaches yield slightly higher performance compared to previously reported approaches based on the duplex, triplex and quadruplex matrix. In fact, the statistical parameters for models obtained with the higher-order and mixed GDI method are superior to those reported in the literature by using other 0-3D QSAR methods. Conclusion: It can be suggested that the higher-order and mixed GDIs, appear as a promissory tool in QSAR/QSPRs, similarity/dissimilarity analysis and virtual screening studies.

Constraints for generating graphs with imposed and forbidden patterns: an application to molecular graphs

Constraints ◽  
2019 ◽  
Vol 25 (1-2) ◽  
pp. 1-22
Author(s):  
Mohamed Amine Omrani ◽  
Wady Naanaa
Keyword(s):  
Molecular Graphs ◽  
Forbidden Patterns

scholarly journals Topological Indices of Para-line Graphs of V-Phenylenic Nanostructures

2019 ◽  
Vol 17 (1) ◽  
pp. 260-266 ◽  
Author(s):  
Imran Nadeem ◽  
Hani Shaker ◽  
Muhammad Hussain ◽  
Asim Naseem
Keyword(s):  
Chemical Properties ◽  
Topological Indices ◽  
Structural Chemistry ◽  
Line Graphs ◽  
Physical And Chemical Properties ◽  
Graph Invariants ◽  
Molecular Graphs ◽  
Physical And Chemical ◽  
And Chemical Properties

Abstract The degree-based topological indices are numerical graph invariants which are used to correlate the physical and chemical properties of a molecule with its structure. Para-line graphs are used to represent the structures of molecules in another way and these representations are important in structural chemistry. In this article, we study certain well-known degree-based topological indices for the para-line graphs of V-Phenylenic 2D lattice, V-Phenylenic nanotube and nanotorus by using the symmetries of their molecular graphs.

The Pt site reactivity of the molecular graphs of Au6Pt isomers

2013 ◽  
Vol 590 ◽  
pp. 41-45 ◽  
Author(s):  
Tianlv Xu ◽  
Samantha Jenkins ◽  
Chen-Xia Xiao ◽  
Julio R. Maza ◽  
Steven R. Kirk
Keyword(s):  
Molecular Graphs
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