eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-09-01
10
3
195
207
10.22052/ijmc.2017.84168.1287
93370
A Novel Molecular Descriptor Derived from Weighted Line Graph
Chandana Adhikari
adhikarichandana@gmail.com
1
Bijay Mishra
bijaym@hotmail.com
2
Sambalpur University
School of Chemistry, Sambalpur University, Jyoti Vihar - 768019
The Bertz indices, derived by counting the number of connecting edges of line graphs of a molecule were used in deriving the QSPR models for the physicochemical properties of alkanes. The inability of these indices to identify the hetero centre in a chemical compound restricted their applications to hydrocarbons only. In the present work, a novel molecular descriptor has been derived from the weighted line graph of the molecular structure and applied in correlating the physicochemical properties of alkane isomers with these descriptors. A weight is tagged at the vertex of the line graph, which consequently modifies the weight of the edge. These descriptors were found to classify the alkane isomers and served well in deriving the QSPR models for various physicochemical properties. The mathematical calculations include the quantitative treatment on the role of substituents (alkyl) in governing the properties under study of the alkane isomers. Further, the use of weighted line graph in the enumeration of the topological index opens up a new vista on application to heteroatomic systems.
https://ijmc.kashanu.ac.ir/article_93370_38c74963a18d68c1715935357d789545.pdf
Weighted line graph
molecular descriptor
Physicochemical properties
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-09-01
10
3
209
222
10.22052/ijmc.2017.34313.1132
98970
Some Topological Indices of Edge Corona of Two Graphs
Chandrashekar Adiga
c_adiga@hotmail.com
1
Malpashree Raju
malpashree.5566@gmail.com
2
Rakshith BIllava Ramanna
ranmsc08@yahoo.co.in
3
Anitha Narasimhamurthy
nanitha@pes.edu
4
University of Mysore, India
University of Mysore, India
University of Mysore, India
PES University, India
In this paper, we compute the Wiener index, first Zagreb index, second<br /> Zagreb index, degree distance index and Gutman index of edge corona of<br /> two graphs. Also in some cases we derive formulas for Weiner index, Zagreb indices, degree distance and Gutman index in terms of vertices and edges .
https://ijmc.kashanu.ac.ir/article_98970_6e2e05bf93818850a77f43d2cfeb1934.pdf
Edge corona
Wiener index
Zagreb indices
Degree distance index
Gutman Index
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-09-01
10
3
223
240
10.22052/ijmc.2019.152413.1400
101675
The distinguishing number and the distinguishing index of graphs from primary subgraphs
Saeid Alikhani
alikhani@yazd.ac.ir
1
Samaneh Soltani
s.soltani1979@gmail.com
2
Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, 89195-741, Yazd, Iran
The distinguishing number (index) <em>D</em>(<em>G</em>) (<em>D</em>'(<em>G</em>)) of a graph <em>G</em> is the least integer <em>d</em> such that <em>G</em> has an vertex labeling (edge labeling) with <em>d</em> labels that is preserved only by a trivial automorphism. Let <em>G</em> be a connected graph constructed from pairwise disjoint connected graphs <em>G</em><sub>1</sub>,... ,<em>G</em><sub>k</sub> by selecting a vertex of <em>G</em><sub>1</sub>, a vertex of <em>G</em><sub>2</sub>, and identifying these two vertices. Then continue in this manner inductively. We say that <em>G</em> is obtained by point-attaching from G<sub>1</sub>, ... ,G<sub>k</sub> and that G<sub>i</sub>'s are the primary subgraphs of <em>G</em>. In this paper, we consider some particular cases of these graphs that are of importance in chemistry and study their distinguishing number and distinguishing index.
https://ijmc.kashanu.ac.ir/article_101675_e08d1f5689447168e1f75217e9827f63.pdf
Distinguishing index
distinguishing number
Chain
Link
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-09-01
10
3
241
249
10.22052/ijmc.2019.149094.1392
101892
The Minimum Estrada Index of Spiro Compounds with k Quadrangles
Mohammad Iranmanesh
iranmanesh@yazd.ac.ir
1
Razieh Nejati
nejati.razieh@gmail.com
2
Yazd University
Yazd University
Abstract. Let G = (<em>V</em>,<em>E</em>) be a finite and simple graph with λ<sub>1</sub>, λ<sub>2</sub>,...,λ<sub>n</sub> as its eigenvalues.The Estrada index of <em>G</em> is EE(G) =∑<em><sup>n</sup></em><sub><em>i</em>=1</sub><em>e</em>^{λ<sub>i</sub>} . A spiro compound is a chemical compound that presents a twisted structure of two or more rings, in which 2 or 3 rings are linked together by one common atom. In this paper, we show that the symmetric and stable spiro compounds among all spiro compounds have the minimum Estrada index.
https://ijmc.kashanu.ac.ir/article_101892_5182c0c753fd3b745f298069defce2ad.pdf
Strada index
spiro compound
point attaching graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-09-01
10
3
251
267
10.22052/ijmc.2017.106402.1325
102016
An upwind local radial basis functions-finite difference (RBF-FD) method for solving compressible Euler equation with application in finite-rate Chemistry
Mostafa Abbaszadeh
m.abbaszadeh@aut.ac.ir
1
Mehdi Dehghan
mdehghan@aut.ac.ir
2
Gholamreza Karamali
gh_karamali@azad.ac.ir
3
Amirkabir University of Technology, Tehran, Iran, Faculty of Mathematics and Computer
Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology,
Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Sience and Technology, South Mehrabad
The main aim of the current paper is to propose an upwind local radial basis functions-finite<br /> difference (RBF-FD) method for solving compressible Euler equation. The mathematical formulation of chemically reacting, inviscid, unsteady flows with species conservation equations<br /> and finite-rate chemistry is studied. The presented technique is based on the developed idea in<br /> [58]. For checking the ability of the new procedure, the compressible Euler equation is solved.<br /> This equation has been classified in category of system of advection-diffusion equations. The<br /> solutions of advection equations have some shock, thus, special numerical methods should be<br /> applied for example discontinuous Galerkin and finite volume methods. Moreover, two problems are given that show the acceptable accuracy and efficiency of the proposed scheme.
https://ijmc.kashanu.ac.ir/article_102016_fe02c8a051aaaa92b3f3b7472e632fba.pdf
Meshless Method
radial basis functions-finite difference (RBF-FD) technique
Compressible Euler equation
finite-rate Chemistry
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2019-09-01
10
3
269
278
10.22052/ijmc.2017.82177.1280
102017
Topological Efficiency of Some Product Graphs
Kannan Pattabiraman
pramank@gmail.com
1
Tholkappian Suganya
suganyatpr@gmail.com
2
Annamalai University
Annamalai University
The topological efficiency index of a connected graph $G,$ denoted by $rho (G),$ is defined as $rho(G)=frac{2W(G)}{left|V(G)right|underline w(G)},$ where $underline w(G)=text { min }left{w_v(G):vin V(G)right}$ and $W(G)$ is the Wiener index of $G.$ In this paper, we obtain the value of topological efficiency index for some composite graphs such as tensor product, strong product, symmetric difference and disjunction of two connected graphs. Further, we have obtained the topological efficiency index for a double graph of a given graph.
https://ijmc.kashanu.ac.ir/article_102017_57332d712f4df9e69475c3fdbbbe8a3c.pdf
Wiener index
topological efficiency index
composite graph