eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-09-01
9
3
167
178
10.22052/ijmc.2018.126056.1353
63663
Rhombellanic Crystals and Quasicrystals
M. Diudea
diudea@gmail.com
1
Babes-Bolyai University, Cluj, Romania
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.
http://ijmc.kashanu.ac.ir/article_63663_b7c423a7aafc69f7061292ced7f52f7c.pdf
Rhombellane
Crystal
Quasicrystal
Topology
Higher rank structure
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-09-01
9
3
179
186
10.22052/ijmc.2018.118091.1342
65124
One-Alpha Descriptor
D. Vukičević
vukicevic@pmfst.hr
1
Z. Yarahmadi
z.yarahmadi@gmail.com
2
University fo Split
islamic azad university
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 .
http://ijmc.kashanu.ac.ir/article_65124_029b38f6f8ef3a2984a420a21466a54a.pdf
One-Alpha descriptor
extermal graph
tree
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-09-01
9
3
187
199
10.22052/ijmc.2018.94933.1306
70501
A new family of high-order difference schemes for the solution of second order boundary value problems
M. Bisheh-Niasar
mbisheh@kashanu.ac.ir
1
A. Saadatmandi
a.saadatmandi@gmail.com
2
M. Akrami-Arani
mostafa_akrami_a@yahoo.com
3
Department of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
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.
http://ijmc.kashanu.ac.ir/article_70501_1b5245ecf65dbca70f307d3ce45217ae.pdf
Boundary value problem
Finite difference methods
Bratu’s problem
Troesch’s problem
High accuracy
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-09-01
9
3
201
212
10.22052/ijmc.2017.69915.1259
70768
On Reciprocal Complementary Wiener Index of a Graph
H. Ramane
hsramane@yahoo.com
1
V. Joshi
vbjoshi.stat@gmail.com
2
V. Manjalapur
vinu.m001@gmail.com
3
S. Shindhe
2shashank.shindhe@gmail.com
4
Karnatak University, Dharwad
Karnatak University, Dharwad
Karnatak University, Dharwad
Karnatak University, Dharwad
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.
http://ijmc.kashanu.ac.ir/article_70768_3f927044a926635c6b3e2ebac79a889b.pdf
Eccentricity
diameter
reciprocal complementary Wiener index
self-centered graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-09-01
9
3
213
225
10.22052/ijmc.2018.126298.1355
70875
The F–Index for some Special Graphs and some Properties of the F–Index
A. Yousefi
naser.yosefi53@yahoo.com
1
A. Iranmanesh
iranmanesh@modares.ac.ir
2
A. Dobrynin
dobr@math.nsc.ru
3
A. Tehranian
tehranian@srbiau.ac.ir
4
Department of Mathematics, Science and Research Branch, Islamic Azad University, P. O. Box 14515 – 1775, Tehran, Iran
Tarbiat Modares University
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia
Islamic Azad University
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.
http://ijmc.kashanu.ac.ir/article_70875_a7168a9c32e5ec25f431f0474ad9c70f.pdf
Forgotten topological index
Edge switching
Edge moving
Edge separating
k–apex tree
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-09-01
9
3
227
239
10.22052/ijmc.2018.141455.1378
73595
On the Bicyclic Graphs with Minimum Reduced Reciprocal Randic Index
A. Ali
akbarali.maths@gmail.com
1
S. Elumalai
sureshkako@gmail.com
2
S. Wang
wangs@savannahstate.edu
3
D. Dimitrov
darko.dimitrov11@gmail.com
4
University of Management & Technology Sialkot, Pakistan
Velammal Engineering College, Surapet, Chennai-66 Tamil Nadu, India
Department of Mathematics, Savannah State University Savannah, GA 31404, USA
Hochschule fur Technik und Wirtschaft, Berlin, Germany and Faculty of Information Studies, Novo Mesto, Slovenia
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.
http://ijmc.kashanu.ac.ir/article_73595_63132a57f5046b8d29de08c6850fb0dc.pdf
Chemical graph theory
molecular structure descriptor
topological index
reduced reciprocal Randić index
bicyclic graph