University of KashanIranian Journal of Mathematical Chemistry2228-648911420201201On the Modified First Zagreb Connection Index of Trees of a Fixed Order and Number of Branching Vertices21322611082710.22052/ijmc.2020.240260.1514ENSadia NoureenNational University of Computer and Emerging Sciences, Lahore, PakistanAkhlaq AhmadBhattiNational University of Computer and
Emerging Sciences, Lahore, PakistanAkbar AliUniversity of Hail, Hail, Saudi Arabia0000-0001-8160-4196Journal Article20200830The modified first Zagreb connection index $ZC_{1}^{*}$ for a graph $G$ is defined as $ZC_{1}^{*}(G)= \sum_{v\in V(G)}d_{v}\tau_{v}\,$, where $d_{v}$ is degree of the vertex $v$ and $\tau _{v}$ is the connection number of $v$ (that is, the number of vertices having distance 2 from $v$). By an $n$-vertex graph, we mean a graph of order $n$. A branching vertex of a graph is a vertex with degree greater than $2$. In this paper, the graphs with maximum and minimum $ZC_{1}^{*}$ values are characterized from the class of all $n$-vertex trees with a fixed number of branching vertices.https://ijmc.kashanu.ac.ir/article_110827_9963a63de0e8366746c57fc8870654ad.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648911420201201Some Properties of the Leap Eccentric Connectivity Index of Graphs22723711128710.22052/ijmc.2020.233343.1505ENLing SongCollege of Mathematics and Statistics
Hunan Normal UniversityLiu HechaoSchool of Mathematics and Statistics, Hunan Normal University,Changsha, HunanTang ZikaiHunan Normal University0000-0002-2577-7890Journal Article20200530The leap eccentric connectivity index of $G$ is defined as $$L\xi^{C}(G)=\sum_{v\in V(G)}d_{2}(v|G)e(v|G)$$ where $d_{2}(v|G) $ be the second degree of the vertex $v$ and $e(v|G)$ be the eccentricity of the vertex $v$ in $G$. In this paper, we give some properties of the leap eccentric connectivity index of the graph $G$.https://ijmc.kashanu.ac.ir/article_111287_4b43297eb60144e50590fd985aba2e95.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648911420201201Odd-Even Effect Observed in the Electro-Optical Properties of the Homologous Series of HnCBP Liquid Crystal Studied under the Impact of the Electric Field: A Theoretical Approach23925411128810.22052/ijmc.2020.232036.1503ENNarinder KumarDepartment of Physics,
School of Physical & Decision Sciences,
Babasaheb Bhimrao Ambedkar University,
Vidya Vihar, Raebareli Road, Lucknow (U.P.) 226025 INDIA0000-0001-8537-0307Pawan SinghDepartment of Physics,
School of Physical & Decision Sciences,
Babasaheb Bhimrao Ambedkar University,
Vidya Vihar, Raebareli Road, Lucknow (U.P.) 226025 INDIA0000-0002-5489-0227Khem ThapaDepartment of Physics,
School of Physical & Decision Sciences,
Babasaheb Bhimrao Ambedkar University,
Vidya Vihar, Raebareli Road, Lucknow (U.P.) 226025 INDIA0000-0003-2639-0652Devesh KumarDepartment of Physics,
School of Physical &amp; Decision Sciences,
Babasaheb Bhimrao Ambedkar University,
Vidya Vihar, Raebareli Road, Lucknow (U.P.) 226025 INDIA
Email:dkclcre@yahoo.com0000-0001-8537-0307Journal Article20200519The liquid crystal (LC) 4-4′-disubstituted biphenyls (HnCBP) of the general line formula HO-(CnH2n+1)-O-C6H4-C6H4-CN (n=1-12) shows the odd-even effect under the applied electric field. The odd-even effects are observed in the HOMO-LUMO gap, birefringence, order parameter, and dipole moment. The odd carbon atom number of alkyl chain shows HOMO-LUMO gap, birefringence and order parameter in the upward direction and even carbon atom number of alkyl chain shows in the downward direction; however the dipole moment exhibits a shift of even carbon number of alkyl chain in the upward direction and odd carbon number of alkyl chain in the downward direction.https://ijmc.kashanu.ac.ir/article_111288_6b5bf4e5913ac3f5e724b666dfd53e0a.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648911420201201Some Indices in the Random Spiro Chains25527011129010.22052/ijmc.2020.231652.1502ENHechao LiuSchool of Mathematics and Statistics, Hunan Normal UniversityMingyao ZengSchool of Mathematics and Statistics, Hunan Normal UniversityHanyuan DengSchool of Mathematics and Statistics, Hunan Normal University0000-0003-1680-2473Zikai TangSchool of Mathematics and Statistics, Hunan Normal University0000-0002-2577-7890Journal Article20200517The Gutman index, Schultz index, multiplicative degree-Kirchhoff index, additive degree-Kirchhoff index are four well-studied topological indices, which are useful tools in QSPR and QSAR investigations. Spiro compounds are an important class of cycloalkanes in organic chemistry. In this paper, we determine the expected values of these indices in the random spiro chains, and the extremal values among all spiro chains with n hexagons.https://ijmc.kashanu.ac.ir/article_111290_ddb466c03fbb7c99e7b639afa7c5f505.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648911420201201The Expected Values of Merrifield-Simmons Index in Random Phenylene Chains27128111129110.22052/ijmc.2020.237192.1508ENLina WeiXinjiang Normal University0000-0003-2824-2338Hong BianDepartment of Mathematics, Xinjiang Normal University,
Urumqi, Xinjiang 830054, P.R.China0000-0003-2824-2338Haizheng YuXinjiang UniversityJili DingXinjiang normal UniversityJournal Article20200628The Merrifield-Simmons index of a graph G is the number of independent sets in G. In this paper, we give exact formulae for the expected value of the Merrifield-Simmons index of random phenylene chains by means of auxiliary graphs.https://ijmc.kashanu.ac.ir/article_111291_fc26675633cc992ed50db53685ba608a.pdf