eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-12-01
10
4
279
293
10.22052/ijmc.2019.200349.1460
102191
On the revised edge-Szeged index of graphs
Hechao Liu
hechaoliu@yeah.net
1
Lihua You
ylhua@scnu.edu.cn
2
Zikai Tang
zikaitang@163.com
3
School of Mathematics and Statistics, Hunan Normal University, Changsha City, Hunan Province, China
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. China
School of Mathematics and Statistics, Hunan Normal University, Changsha City, Hunan Province, China
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.
https://ijmc.kashanu.ac.ir/article_102191_dd77ab587a307bd7e4971623d96ef182.pdf
Revised edge-Szeged index
Conjugated unicyclic graph
Join graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-12-01
10
4
295
305
10.22052/ijmc.2019.169508.1420
102447
On the Graovac-Ghorbani index
Modjtaba Ghorbani
mghorbani@sru.ac.ir
1
Shaghayegh Rahmani
s.rahmani@sru.ac.ir
2
Ottorino Ori
ottorino.ori@gmail.com
3
Department of mathematics, Shahid Rajaee Teacher Training University
Department of Mathematics, SRTT University
Actinum Chemical Research, Italy
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.
https://ijmc.kashanu.ac.ir/article_102447_320bebdec70cf381ee9f7a601e0ce167.pdf
Atom bond connectivity index
Molecular graphs
topological index
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-12-01
10
4
307
318
10.22052/ijmc.2019.174722.1432
102512
Some Results on Forgotten Topological Coindex
Mahdieh Azari
mahdie.azari@gmail.com
1
Farzaneh Falahati-Nezhed
farzanehfalahati_n@yahoo.com
2
Kazerun Branch, Islamic Azad University
Safadasht Branch, Islamic Azad University
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.
https://ijmc.kashanu.ac.ir/article_102512_f335e16389378c0cec788b4cc1719e46.pdf
vertex degree
Bound
graph invariant
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-12-01
10
4
319
330
10.22052/ijmc.2019.195759.1456
102513
On generalized atom-bond connectivity index of cacti
Fazal Hayat
fhayatmaths@gmail.com
1
School of Mathematical Sciences, South China Normal University,
Guangzhou 510631, PR China
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.
https://ijmc.kashanu.ac.ir/article_102513_935bc1ec217d14c2928b98f54b69e2c5.pdf
Atom-bond connectivity index
Cactus
Extremal graph
Pendant vertices
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-12-01
10
4
331
341
10.22052/ijmc.2019.191865.1448
102514
QSPR Analysis with Curvilinear Regression Modeling and Topological Indices
Ozge Havare
ozgeeclkgl@gmail.com
1
Mersin University
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.
https://ijmc.kashanu.ac.ir/article_102514_07ce16949e9353fa46630d934daf4926.pdf
Gutman Index
Product connectivity Banhatti index
Variance of degree index
Sigma index
QSPR
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-12-01
10
4
343
360
10.22052/ijmc.2019.191800.1447
102515
The number of maximal matchings in polyphenylene chains
Taylor Short
taylor.m.short@gmail.com
1
Zachary Ash
ash@mail.gvsu.edu
2
Department of Mathematics, Grand Valley State University, Allendale, MI, USA
Department of Mathematics, Grand Valley State University, Allendale, MI, USA
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.
https://ijmc.kashanu.ac.ir/article_102515_9b04a5b392e022baa61e816c10095e99.pdf
Matching
maximal
polyphenylene chain