On the revised edge-Szeged index of graphs Hechao Liu School of Mathematics and Statistics, Hunan Normal University, Changsha City, Hunan Province, China author Lihua You School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P.R. China author Zikai Tang School of Mathematics and Statistics, Hunan Normal University, Changsha City, Hunan Province, China author text article 2019 eng The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of edges of G lying closer to vertex v than to vertex u, and the number of edges equidistant to u and v. 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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 10 v. 4 no. 2019 279 293 http://ijmc.kashanu.ac.ir/article_102191_dd77ab587a307bd7e4971623d96ef182.pdf dx.doi.org/10.22052/ijmc.2019.200349.1460 On the Graovac-Ghorbani index Modjtaba Ghorbani Department of mathematics, Shahid Rajaee Teacher Training University author Shaghayegh Rahmani Department of Mathematics, SRTT University author Ottorino Ori Actinum Chemical Research, Italy author text article 2019 eng For the edge e = uv of a graph G, let nu = n(u|G) be the number of vertices of G lying closer to the vertex u than to the vertex v and nv= n(v|G) can be defined simailarly. Then the ABCGG index of G is defined as ABCGG =\sum_{e=uv} \sqrt{f(u,v)}, where f(u,v)= (nu+nv-2)/nunvThe aim of this paper is to give some new results on this graph invariant. We also calculate the ABCGG of an infinite family of fullerenes. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 10 v. 4 no. 2019 295 305 http://ijmc.kashanu.ac.ir/article_102447_320bebdec70cf381ee9f7a601e0ce167.pdf dx.doi.org/10.22052/ijmc.2019.169508.1420 Some Results on Forgotten Topological Coindex Mahdieh Azari Kazerun Branch, Islamic Azad University author Farzaneh Falahati-Nezhed Safadasht Branch, Islamic Azad University author text article 2019 eng The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. 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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 10 v. 4 no. 2019 307 318 http://ijmc.kashanu.ac.ir/article_102512_f335e16389378c0cec788b4cc1719e46.pdf dx.doi.org/10.22052/ijmc.2019.174722.1432 On generalized atom-bond connectivity index of cacti Fazal Hayat School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China author text article 2019 eng The generalized atom-bond connectivity index of a graph G is denoted by ABCa(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))aa$over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for ABCa index for cacti of order$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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 10 v. 4 no. 2019 319 330 http://ijmc.kashanu.ac.ir/article_102513_935bc1ec217d14c2928b98f54b69e2c5.pdf dx.doi.org/10.22052/ijmc.2019.195759.1456 QSPR Analysis with Curvilinear Regression Modeling and Topological Indices Ozge Havare Mersin University author text article 2019 eng 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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 10 v. 4 no. 2019 331 341 http://ijmc.kashanu.ac.ir/article_102514_07ce16949e9353fa46630d934daf4926.pdf dx.doi.org/10.22052/ijmc.2019.191865.1448 The number of maximal matchings in polyphenylene chains Taylor Short Department of Mathematics, Grand Valley State University, Allendale, MI, USA author Zachary Ash Department of Mathematics, Grand Valley State University, Allendale, MI, USA author text article 2019 eng 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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 10 v. 4 no. 2019 343 360 http://ijmc.kashanu.ac.ir/article_102515_9b04a5b392e022baa61e816c10095e99.pdf dx.doi.org/10.22052/ijmc.2019.191800.1447