University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
9
3
2018
09
01
Rhombellanic Crystals and Quasicrystals
167
178
EN
M.
V.
Diudea
Babes-Bolyai University, Cluj, Romania
diudea@gmail.com
10.22052/ijmc.2018.126056.1353
Design of some crystal and quasicrystal networks, based on rhombellane tiling,is presented. [1,1,1]Propellane,is a synthesized organic molecule; its hydrogenated form, the bicyclo[1.1.1]pentane,may be represented by the complete bipartite graph K2,3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, connectivity sequence, ring sequence and map operations relating structures to their seeds. It is shown, by alternating sum of ranked substructures, that radial structures represent complex constructions of higher rank. Basic properties of rhombellanes, coloring included, are outlined.
Rhombellane,Crystal,Quasicrystal,Topology,Higher rank structure
http://ijmc.kashanu.ac.ir/article_63663.html
http://ijmc.kashanu.ac.ir/article_63663_b7c423a7aafc69f7061292ced7f52f7c.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
9
3
2018
09
01
One-Alpha Descriptor
179
186
EN
D.
Vukičević
University fo Split
vukicevic@pmfst.hr
Z.
Yarahmadi
islamic azad university
z.yarahmadi@gmail.com
10.22052/ijmc.2018.118091.1342
Recently, one-two descriptor has been defined and it has been shown that it is a good predictor of the heat capacity at P constant (CP) and of the total surface area (TSA). In this paper, we analyze its generalizations by replacing the value 2 by arbitrary positive value . We show that these analyses may be on interest, because even good predictions of CP and TSA can be slightly improved. Furthermore, it can be expected that this more general descriptor can find a wider range of application than the original one. The extremal values of trees have been found for all values of .
One-Alpha descriptor,extermal graph,tree
http://ijmc.kashanu.ac.ir/article_65124.html
http://ijmc.kashanu.ac.ir/article_65124_029b38f6f8ef3a2984a420a21466a54a.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
9
3
2018
09
01
A new family of high-order difference schemes for the solution of second order boundary value problems
187
199
EN
M.
Bisheh-Niasar
Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran
mbisheh@kashanu.ac.ir
A.
Saadatmandi
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
a.saadatmandi@gmail.com
M.
Akrami-Arani
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
mostafa_akrami_a@yahoo.com
10.22052/ijmc.2018.94933.1306
Many problems in chemistry, nanotechnology, biology, natural science, chemical physics and engineering are modeled by two point boundary value problems. In general, analytical solution of these problems does not exist. In this paper, we propose a new class of high-order accurate methods for solving special second order nonlinear two point boundary value problems. Local truncation errors of these methods are discussed. To illustrate the potential of the new methods, we apply them for solving some well-known problems, including Troesch’s problem, Bratu’s problem and certain singularly perturbed problem. Bratu’s problem and Troech’s problems, may be used to model some chemical reaction-diffusion and heat transfer processes. We also compare the results of this work with some existing results in the literature and show that the new methods are efficient and applicable.
Boundary value problem,Finite difference methods,Bratu’s problem,Troesch’s problem,High accuracy
http://ijmc.kashanu.ac.ir/article_70501.html
http://ijmc.kashanu.ac.ir/article_70501_1b5245ecf65dbca70f307d3ce45217ae.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
9
3
2018
09
01
On Reciprocal Complementary Wiener Index of a Graph
201
212
EN
H.
S.
Ramane
Karnatak University, Dharwad
hsramane@yahoo.com
V.
B.
Joshi
Karnatak University, Dharwad
vbjoshi.stat@gmail.com
V.
V.
Manjalapur
Karnatak University, Dharwad
vinu.m001@gmail.com
S.
D.
Shindhe
Karnatak University, Dharwad
2shashank.shindhe@gmail.com
10.22052/ijmc.2017.69915.1259
The eccentricity of a vertex v of graph G is the largest distance between and any other vertex of a graph . The reciprocal complementary Wiener (RCW) index of is defined as,<br /> ,<br /> where D is the diameter of G and is the distance between the vertices and . In this paper we have obtained bounds for the index in terms of eccentricities and given an algorithm to compute the index.
Eccentricity,diameter,reciprocal complementary Wiener index,self-centered graph
http://ijmc.kashanu.ac.ir/article_70768.html
http://ijmc.kashanu.ac.ir/article_70768_3f927044a926635c6b3e2ebac79a889b.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
9
3
2018
09
01
The F–Index for some Special Graphs and some Properties of the F–Index
213
225
EN
A.
Yousefi
Department of Mathematics, Science and Research Branch, Islamic Azad University,
P. O. Box 14515 – 1775, Tehran, Iran
naser.yosefi53@yahoo.com
A.
Iranmanesh
Tarbiat Modares University
iranmanesh@modares.ac.ir
A.
A.
Dobrynin
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia
dobr@math.nsc.ru
A.
Tehranian
Islamic Azad University
tehranian@srbiau.ac.ir
10.22052/ijmc.2018.126298.1355
The "forgotten topological index" or "F–index" has been introduced by Furtula and Gutman in 2015. The F–index of a (molecular) graph is defined as the sum of cubes of the vertex degrees of the graph. In this paper, we compute this topological index for some special graphs such as Wheel graph, Barbell graph and Friendship graph. Moreover, the effects on the F–index are observed when some operations such as edge switching, edge moving and edge separating are applied to the graphs. Finally, we investigate degeneracy of F–index for small graphs.
Forgotten topological index,Edge switching,Edge moving,Edge separating,k–apex tree
http://ijmc.kashanu.ac.ir/article_70875.html
http://ijmc.kashanu.ac.ir/article_70875_a7168a9c32e5ec25f431f0474ad9c70f.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
9
3
2018
09
01
On the Bicyclic Graphs with Minimum Reduced Reciprocal Randic Index
227
239
EN
A.
Ali
0000-0001-8160-4196
University of Management & Technology Sialkot, Pakistan
akbarali.maths@gmail.com
S.
Elumalai
Velammal Engineering College, Surapet, Chennai-66 Tamil Nadu, India
sureshkako@gmail.com
S.
Wang
Department of Mathematics, Savannah State University Savannah, GA 31404, USA
wangs@savannahstate.edu
D.
Dimitrov
Hochschule fur Technik und Wirtschaft, Berlin, Germany
and
Faculty of Information Studies, Novo Mesto, Slovenia
darko.dimitrov11@gmail.com
10.22052/ijmc.2018.141455.1378
The reduced reciprocal Randić (RRR) index is a molecular structure descriptor (or more precisely, a topological index), which is useful for predicting the standard enthalpy of formation and normal boiling point of isomeric octanes. In this paper, a mathematical aspect of RRR index is explored, or more specifically, the graph(s) having minimum RRR index is/are identified from the collection of all n–vertex connected bicyclic graphs for n≥5. As a consequence, the best possible lower bound on the RRR index, for n–vertex connected bicyclic graphs is obtained when n≥5.
Chemical graph theory,molecular structure descriptor,topological index,reduced reciprocal Randić index,bicyclic graph
http://ijmc.kashanu.ac.ir/article_73595.html
http://ijmc.kashanu.ac.ir/article_73595_63132a57f5046b8d29de08c6850fb0dc.pdf