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Symmetry
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Analytical and Computational Properties of Topological Indices II
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Analytical and Computational Properties of Topological Indices II

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 March 2022) | Viewed by 7058

Special Issue Editors

Prof. Dr. Jose M. Rodriguez

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Guest Editor
Department of Mathematics, Carlos III University of Madrid-Leganés Campus, Avenida de la Universidad 30, CP-28911, Leganés, Madrid, Spain
Interests: discrete mathematics; fractional calculus; topological indices; polynomials in graphs; geometric function theory; geometry; approximation theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Eva Tourís

E-Mail Website
Guest Editor
Department of Mathematics, Science Faculty, Autónoma University of Madrid, Cantoblanco Campus, CP-28049 Madrid, Spain
Interests: network theory; discrete mathematics; topological indices; functions of a complex variable; potential theory; approximation theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Although Topological Indices have played an important role in Mathematical Chemistry since the seminal work of Wiener in 1947, in recent years, this role has significantly increased. On the one side, molecular descriptors constitute an aid tool in Chemistry, especially in QSPR/QSAR investigations. On the other side, they have become an important part of some areas of Mathematics, as Graph Theory; this interest has been recognized in the 2020-version of the Mathematical Subject Classification by including two new areas: 05C09 - Graphical indices (Wiener index, Zagreb index, Randić index, etc.), and 05C92 - Chemical graph theory.

The aim of this Special Issue is to attract leading researchers in this area in order to include new results on these topics, both from a theoretical and an applied point of view.

Prof. Dr. Jose M. Rodriguez
Prof. Dr. Eva Tourís
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • topological indices
  • graphical indices
  • chemical graph theory
  • mathematical chemistry
  • topological descriptors
  • molecular descriptors
  • graph optimization problems
  • polynomials on topological indices

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Published Papers (3 papers)

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Research

18 pages, 941 KiB  
Article
New Versions of Locating Indices and Their Significance in Predicting the Physicochemical Properties of Benzenoid Hydrocarbons
by Suha Wazzan and Anwar Saleh
Symmetry 2022, 14(5), 1022; https://doi.org/10.3390/sym14051022 - 17 May 2022
Cited by 7 | Viewed by 2515
Abstract
In this paper, we introduce some new versions based on the locating vectors named locating indices. In particular, Hyper locating indices, Randić locating index, and Sambor locating index. The exact formulae for these indices of some well-known families of graphs and for the [...] Read more.
In this paper, we introduce some new versions based on the locating vectors named locating indices. In particular, Hyper locating indices, Randić locating index, and Sambor locating index. The exact formulae for these indices of some well-known families of graphs and for the Helm graph are derived. Moreover, we determine the importance of these locating indices for 11 benzenoid hydrocarbons. Furthermore, we show that these new versions of locating indices have a reasonable correlation using linear regression with physicochemical characteristics such as molar entropy, acentric factor, boiling point, complexity, octanol–water partition coefficient, and Kovats retention index. The cases in which good correlations were obtained suggested the validity of the calculated topological indices to be further used to predict the physicochemical properties of much more complicated chemical compounds. Full article
(This article belongs to the Special Issue Analytical and Computational Properties of Topological Indices II)
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13 pages, 325 KiB  
Article
Sharp Upper and Lower Bounds of VDB Topological Indices of Digraphs
by Juan Monsalve and Juan Rada
Symmetry 2021, 13(10), 1903; https://doi.org/10.3390/sym13101903 - 9 Oct 2021
Cited by 11 | Viewed by 1548
Abstract
A vertex-degree-based (VDB, for short) topological index φ induced by the numbers φij was recently defined for a digraph D, as φD=12∑uvφdu+dv−, where [...] Read more.
A vertex-degree-based (VDB, for short) topological index φ induced by the numbers φij was recently defined for a digraph D, as φD=12∑uvφdu+dv−, where du+ denotes the out-degree of the vertex u,dv− denotes the in-degree of the vertex v, and the sum runs over the set of arcs uv of D. This definition generalizes the concept of a VDB topological index of a graph. In a general setting, we find sharp lower and upper bounds of a symmetric VDB topological index over Dn, the set of all digraphs with n non-isolated vertices. Applications to well-known topological indices are deduced. We also determine extremal values of symmetric VDB topological indices over OTn and OG, the set of oriented trees with n vertices, and the set of all orientations of a fixed graph G, respectively. Full article
(This article belongs to the Special Issue Analytical and Computational Properties of Topological Indices II)
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13 pages, 326 KiB  
Article
On a Conjecture about the Sombor Index of Graphs
by Kinkar Chandra Das, Ali Ghalavand and Ali Reza Ashrafi
Symmetry 2021, 13(10), 1830; https://doi.org/10.3390/sym13101830 - 1 Oct 2021
Cited by 17 | Viewed by 2086
Abstract
Let G be a graph with vertex set V(G) and edge set E(G). A graph invariant for G is a number related to the structure of G which is invariant under the symmetry of G. [...] Read more.
Let G be a graph with vertex set V(G) and edge set E(G). A graph invariant for G is a number related to the structure of G which is invariant under the symmetry of G. The Sombor and reduced Sombor indices of G are two new graph invariants defined as SO(G)=∑uv∈E(G)dG(u)2+dG(v)2 and SOred(G)=∑uv∈E(G)dG(u)−12+dG(v)−12, respectively, where dG(v) is the degree of the vertex v in G. We denote by Hn,ν the graph constructed from the star Sn by adding ν edge(s), 0≤ν≤n−2, between a fixed pendent vertex and ν other pendent vertices. Réti et al. [T. Réti, T Došlić and A. Ali, On the Sombor index of graphs, Contrib. Math.3 (2021) 11–18] proposed a conjecture that the graph Hn,ν has the maximum Sombor index among all connected ν-cyclic graphs of order n, where 0≤ν≤n−2. In some earlier works, the validity of this conjecture was proved for ν≤5. In this paper, we confirm that this conjecture is true, when ν=6. The Sombor index in the case that the number of pendent vertices is less than or equal to n−ν−2 is investigated, and the same results are obtained for the reduced Sombor index. Some relationships between Sombor, reduced Sombor, and first Zagreb indices of graphs are also obtained. Full article
(This article belongs to the Special Issue Analytical and Computational Properties of Topological Indices II)
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