University of KashanIranian Journal of Mathematical Chemistry2228-648914120230301In Memory of Professor Ali Reza Ashrafi (1964-2023): A Matchless Role Model in Mathematical Chemistry in Iran1611378110.22052/ijmc.2023.253009.1726ENSaeidAlikhaniDepartment of Mathematical Sciences, Yazd University, 89195-741, Yazd, I.R. Iran0000-0002-1801-203XMarziehPourbabaeeDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran0000-0003-1828-5991ModjtabaGhorbaniDepartment of mathematics, Shahid Rajaee Teacher Training University0000-0002-5324-0847AbbasSaadatmandiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, Iran0000-0002-7744-7770Journal Article20230603https://ijmc.kashanu.ac.ir/article_113781_1a67c3acb2b22badfd24d728b6641f4b.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914120230301On the Number of Perfect Star Packing and Perfect Pseudo Matching in Some Fullerene Graphs71811378210.22052/ijmc.2022.248451.1669ENMeysamTaheri-DehkordiUniversity of Applied Science and Technology (UAST), Tehran, IRAN0000-0002-6085-2622Gholam HosseinFath-TabarDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran0000-0003-1105-3020Journal Article20221017A perfect star packing in a fullerene graph G is a spanning subgraph of G whose every component is isomorphic to the star graph K_1,3. A perfect pseudo matching of a fullerene graph G is a spanning subgraph H of G such that each component of H is either K_2 or K_1,3. In this paper, we examine the number of perfect star packing in (3,6)-fullerene graphs and perfect pseudo matching in chamfered fullerene graphs.https://ijmc.kashanu.ac.ir/article_113782_dfb7cf23b0df76f5cbc228ac644a1ecb.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914120230301On General Degree-Eccentricity Index For Trees with Fixed Diameter and Number of Pendent Vertices193211378310.22052/ijmc.2023.248566.1675ENMesfin MasreLegeseDepartment of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia0000-0002-2103-8847Journal Article20221117The general degree-eccentricity index of a graph $G$ is defined by,<br />$DEI_{a,b} (G) = \sum_{v \in V(G)} d_{G}^{a}(v) ecc_{G}^{b}(v)$ for $a, b \in \mathbb{R}$, where $V(G)$ is the vertex set of $G$, $ecc_{G}(v)$ is the eccentricity of a vertex $v$ and $d_{G}(v)$ is the degree of $v$ in $G$.<br /><br />In this paper, we generalize results on the general eccentric connectivity index for<br />trees.<br />We present upper and lower bounds on the general degree-eccentricity index for trees of given order and diameter, and trees of given order and number of pendant vertices.<br />The upper bounds hold for $a > 1$ and $b \in \mathbb{R}\setminus\{0\}$ and<br />the lower bounds holds for $0 < a < 1$ and $b \in \mathbb{R}\setminus\{0\}$.<br />We include the case $a = 1$ and $b \in \{-1, 1\}$ in those theorems for which the proof of that case is not complicated.<br />We present all the extremal graphs, which means that our bounds are best possible.https://ijmc.kashanu.ac.ir/article_113783_457519ec6e72467b35be4219b7d54e71.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914120230301Entire Sombor Index of Graphs334511378410.22052/ijmc.2022.248350.1663ENFatemeMovahediGolestan UniversityMohammad HadiAkhbariIslamic Azad UniversityJournal Article20220924Let $G=(V, E)$ be a simple graph with vertex set $V$ and edge set $E$. The Sombor index of the graph $G$ is a degree-based topological index, defined as<br />$$SO(G)=\sum_{uv \in E}\sqrt{d(u)^2+d(v)^2},$$<br />in which $d(x)$ is the degree of the vertex $x \in V$ for $x=u, v$. \\<br />In this paper, we introduce a new topological index called the entire Sombor index of a graph which is defined as the sum of the terms $\sqrt{d(x)^2+d(y)^2}$ where $x$ is either adjacent or incident to $y$ and $x, y \in V \cup E$. We obtain exact values of this new topological index in some graphs families. Some important properties of this index are obtained.https://ijmc.kashanu.ac.ir/article_113784_6f555b89eac722e52fdcf492d507111c.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914120230301Edge Metric Dimension of Fullerenes475411378510.22052/ijmc.2022.248392.1666ENParvaneBonyabadiDepartment of pure Mathematics, Faculty of Mathematical Sciences,\\
Ferdowsi University of Mashhad, P.O.\ Box 1159, Mashhad 91775, IranKazemKhashyarmaneshDep. of Math.
Ferdowsi University of Mashhad0000-0003-3314-7298MostafaTavakoliFerdowsi University of Mashhad, I R IranMojganAfkhamiDepartment of Mathematics, University of Neyshabur,
P.O.Box 91136-899, Neyshabur, IranJournal Article20221003A $(k,6)$-fullerene graph is a planar $3$-connected cubic graph whose faces are $k$-gons and hexagons. The aim of this paper is to study the edge metric dimension of $(3,6)$- and $(4,6)$-fullerene graphs.https://ijmc.kashanu.ac.ir/article_113785_b23e96070e02dc7f5b103efc7b491f6b.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648914120230301Finding the $V_2(555 − 777)$ Double Vacancy Defect in Graphene Using Rotational Symmetry556411379110.22052/ijmc.2023.247422.1653ENMargaret LynArchibaldThe John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University
of the Witwatersrand, Private Bag 3, P O WITS 2050, South Africa0000-0001-5635-6733SonjaCurrieThe John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University
of the Witwatersrand, Private Bag 3, P O WITS 2050, South Africa0000 0003 2190 8862MarlenaNowaczykAGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059
Krakow, Poland0000 0003 3657 1609Journal Article20220825We use the underlying hexagonal structure of graphene to identify uniquely the<br />position pertaining to a divacancy defect of type $V_2(555 − 777)$. This is achieved by<br />considering at most three closed path readings and the symmetry of the defective structure. We work in the corresponding rectangular model but still rely on the rotational<br />symmetry of the original hexagonal grid. Our approach is purely mathematical and<br />therefore there is no need for imaging technologies.https://ijmc.kashanu.ac.ir/article_113791_2ebfae39fdbdc1fa3851df9221e9e47c.pdf