University of KashanIranian Journal of Mathematical Chemistry2228-648910420191201On the Revised Edge-Szeged Index of Graphs27929310219110.22052/ijmc.2019.200349.1460ENHechaoLiuSchool of Mathematics and Statistics, Hunan Normal University, Changsha City, Hunan Province, China0000-0001-7606-4842LihuaYouSchool of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. ChinaZikaiTangSchool of Mathematics and Statistics, Hunan Normal University, Changsha City, Hunan Province, China0000-0002-2577-7890Journal Article20190903The 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.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648910420191201On the Graovac-Ghorbani Index29530510244710.22052/ijmc.2019.169508.1420ENModjtabaGhorbaniDepartment of mathematics, Shahid Rajaee Teacher Training University0000-0002-5324-0847ShaghayeghRahmaniDepartment of Mathematics, SRTT UniversityOttorinoOriActinum Chemical Research, ItalyJournal Article20190126For 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.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648910420191201Some Results on Forgotten Topological Coindex30731810251210.22052/ijmc.2019.174722.1432ENMahdiehAzariKazerun Branch, Islamic Azad University0000-0002-0919-0598FarzanehFalahati-NezhedSafadasht Branch, Islamic Azad UniversityJournal Article20190310The 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.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648910420191201On Generalized Atom-bond Connectivity Index of Cacti31933010251310.22052/ijmc.2019.195759.1456ENFazalHayatSchool of Mathematical Sciences, South China Normal University,
Guangzhou 510631, PR ChinaJournal Article20190725The 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.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648910420191201QSPR Analysis with Curvilinear Regression Modeling and Topological Indices33134110251410.22052/ijmc.2019.191865.1448ENOzge ColakogluHavareMersin UniversityJournal Article20190628Topological 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.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648910420191201The Number of Maximal Matchings in Polyphenylene Chains34336010251510.22052/ijmc.2019.191800.1447ENTaylorShortDepartment of Mathematics, Grand Valley State University, Allendale, MI, USAZacharyAshDepartment of Mathematics, Grand Valley State University, Allendale, MI, USAJournal Article20190627A 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