University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
10
4
2019
12
01
On the revised edge-Szeged index of graphs
279
293
EN
Hechao
Liu
0000-0001-7606-4842
School of Mathematics and Statistics, Hunan Normal University, Changsha City, Hunan Province, China
hechaoliu@yeah.net
Lihua
You
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. China
ylhua@scnu.edu.cn
Zikai
Tang
0000-0002-2577-7890
School of Mathematics and Statistics, Hunan Normal University, Changsha City, Hunan Province, China
zikaitang@163.com
10.22052/ijmc.2019.200349.1460
The revised edge-Szeged index of a connected graph $G$ is defined as Sz<sub>e</sub>*(G)=∑<sub>e=uv∊E(G)</sub>( (m<sub>u</sub>(e|G)+(m<sub>0</sub>(e|G)/2)(m<sub>v</sub>(e|G)+(m<sub>0</sub>(e|G)/2) ), where m<sub>u</sub>(e|G), m<sub>v</sub>(e|G) and m<sub>0</sub>(e|G) are, respectively, the number of edges of <em>G</em> lying closer to vertex <em>u</em> than to vertex <em>v</em>, the number of edges of <em>G</em> lying closer to vertex <em>v</em> than to vertex <em>u</em>, and the number of edges equidistant to <em>u</em> and <em>v</em>. In this paper, we give an effective method for computing the revised edge-Szeged index of unicyclic graphs and using this result we identify the minimum revised edge-Szeged index of conjugated unicyclic graphs (i.e., unicyclic graphs with a perfect matching). We also give a method of calculating revised edge-Szeged index of the joint graph.
Revised edge-Szeged index,Conjugated unicyclic graph,Join graph
https://ijmc.kashanu.ac.ir/article_102191.html
https://ijmc.kashanu.ac.ir/article_102191_dd77ab587a307bd7e4971623d96ef182.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
10
4
2019
12
01
On the Graovac-Ghorbani index
295
305
EN
Modjtaba
Ghorbani
Department of mathematics, Shahid Rajaee Teacher Training University
mghorbani@sru.ac.ir
Shaghayegh
Rahmani
Department of Mathematics, SRTT University
s.rahmani@sru.ac.ir
Ottorino
Ori
Actinum Chemical Research, Italy
ottorino.ori@gmail.com
10.22052/ijmc.2019.169508.1420
For the edge <em>e </em>= <em>uv </em>of a graph <em>G</em>, let <em>n<sub>u</sub></em> = <em>n</em>(<em>u</em>|<em>G</em>) be the number of vertices of <em>G</em> lying closer to the vertex <em>u</em> than to the vertex <em>v</em> and <em>n<sub>v</sub></em>=<em> n</em>(<em>v</em>|<em>G</em>) can be defined simailarly. Then the ABC<em><sub>GG</sub></em> index of <em>G</em> is defined as ABC<em><sub>GG</sub></em> =sum_{e=uv} sqrt{f(u,v)}, where f(u,v)= (n<sub>u</sub>+n<sub>v</sub>-2)/n<sub>u</sub>n<sub>v</sub>The aim of this paper is to give some new results on this graph invariant. We also calculate the ABC<em><sub>GG</sub></em> of an infinite family of fullerenes.
Atom bond connectivity index,Molecular graphs,topological index
https://ijmc.kashanu.ac.ir/article_102447.html
https://ijmc.kashanu.ac.ir/article_102447_320bebdec70cf381ee9f7a601e0ce167.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
10
4
2019
12
01
Some Results on Forgotten Topological Coindex
307
318
EN
Mahdieh
Azari
Kazerun Branch, Islamic Azad University
mahdie.azari@gmail.com
Farzaneh
Falahati-Nezhed
Safadasht Branch, Islamic Azad University
farzanehfalahati_n@yahoo.com
10.22052/ijmc.2019.174722.1432
The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph <em>G</em> as the sum of the terms <em>d<sub>u</sub></em><sup>2</sup>+<em>d<sub>v</sub></em><sup>2</sup> over all non-adjacent vertex pairs <em>uv</em> of <em>G</em>, where <em>d<sub>u</sub></em> denotes the degree of the vertex <em>u</em> in <em>G</em>. In this paper, we present some inequalities for the forgotten topological coindex in terms of some graph parameters such as the order, size, number of pendent vertices, minimal and maximal vertex degrees, and minimal non-pendent vertex degree. We also study the relation between this invariant and some well-known graph invariants such as the Zagreb indices and coindices, multiplicative Zagreb indices and coindices, Zagreb eccentricity indices, eccentric connectivity index and coindex, and total eccentricity. Exact formulae for computing the forgotten topological coindex of double graphs and extended double cover of a given graph are also proposed.
vertex degree,Bound,graph invariant
https://ijmc.kashanu.ac.ir/article_102512.html
https://ijmc.kashanu.ac.ir/article_102512_f335e16389378c0cec788b4cc1719e46.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
10
4
2019
12
01
On generalized atom-bond connectivity index of cacti
319
330
EN
Fazal
Hayat
School of Mathematical Sciences, South China Normal University,
Guangzhou 510631, PR China
fhayatmaths@gmail.com
10.22052/ijmc.2019.195759.1456
The generalized atom-bond connectivity index of a graph <em>G</em> is denoted by ABC<em><sub>a</sub></em>(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))<sup><em><sub>a</sub></em></sup>a$ over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for ABC<em><sub>a</sub></em> index for cacti of order $n$ with fixed number of cycles and for cacti of order $n$ with given number of pendant vertices. Furthermore, we identify all the cacti that achieve the bounds.
Atom-bond connectivity index,Cactus,Extremal graph,Pendant vertices
https://ijmc.kashanu.ac.ir/article_102513.html
https://ijmc.kashanu.ac.ir/article_102513_935bc1ec217d14c2928b98f54b69e2c5.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
10
4
2019
12
01
QSPR Analysis with Curvilinear Regression Modeling and Topological Indices
331
341
EN
Ozge
Colakoglu
Havare
Mersin University
ozgeeclkgl@gmail.com
10.22052/ijmc.2019.191865.1448
Topological indices are the real number of a molecular structure obtained via molecular graph G. Topological indices are used for QSPR, QSAR and structural design in chemistry, nanotechnology, and pharmacology. Moreover, physicochemical properties such as the boiling point, the enthalpy of vaporization, and stability can be estimated by QSAR/QSPR models. In this study, the QSPR (Quantitative Structure-Property Relationship) models were designed using the Gutman index, the product connectivity Banhatti index, the Variance of degree index, and the Sigma index to predict the thermodynamic properties of monocarboxylic acids. The relationship analyses between the thermodynamic properties and the topological indices were done by using the curvilinear regression method. It is used with the linear, quadratic and cubic equations of the curvilinear regression model. These regression models were then compared.
Gutman Index,Product connectivity Banhatti index,Variance of degree index,Sigma index,QSPR
https://ijmc.kashanu.ac.ir/article_102514.html
https://ijmc.kashanu.ac.ir/article_102514_07ce16949e9353fa46630d934daf4926.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
10
4
2019
12
01
The number of maximal matchings in polyphenylene chains
343
360
EN
Taylor
Short
Department of Mathematics, Grand Valley State University, Allendale, MI, USA
taylor.m.short@gmail.com
Zachary
Ash
Department of Mathematics, Grand Valley State University, Allendale, MI, USA
ash@mail.gvsu.edu
10.22052/ijmc.2019.191800.1447
A matching is maximal if no other matching contains it as a proper subset. Maximal matchings model phenomena across many disciplines, including applications within chemistry. In this paper, we study maximal matchings in an important class of chemical compounds: polyphenylenes. In particular, we determine the extremal polyphenylene chains in regards to the number of maximal matchings. We also determine recurrences and generating functions for the sequences enumerating maximal matchings in several specific types of polyphenylenes and use these results to analyze the asymptotic behavior.
Matching,maximal,polyphenylene chain
https://ijmc.kashanu.ac.ir/article_102515.html
https://ijmc.kashanu.ac.ir/article_102515_9b04a5b392e022baa61e816c10095e99.pdf