University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
1
2017
03
01
Stirling Numbers and Generalized Zagreb Indices
1
5
EN
T.
Doslic
1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb,
doslic@grad.hr
S.
Sedghi
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshar, Iran
sedghi_gh@yahoo.com
N.
Shobe
Department of Mathematics, Babol Branch,
Islamic Azad
University, Babol, Iran
nabi_shobe@yahoo.com
10.22052/ijmc.2017.15092
We show how generalized Zagreb indices $M_1^k(G)$ can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.
Simple Graph,Zagreb index,Stirling number
http://ijmc.kashanu.ac.ir/article_15092.html
http://ijmc.kashanu.ac.ir/article_15092_004e2848d32ee0215ed2fb32745ab419.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
1
2017
03
01
Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications
7
23
EN
F.
Taghvaee
University of Kashan
taghvaei19@yahoo.com
G.
Fath-Tabar
University of Kashan
fathtabar@kashanu.ac.ir
10.22052/ijmc.2017.15093
ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matching polynomial, (-1)^km(G, k), in a regular graph. In the rest of this paper, we apply these relations for finding 5,6-matchings of fullerene graphs.
Characteristic polynomial,Matching polynomial,Fullerene graph
http://ijmc.kashanu.ac.ir/article_15093.html
http://ijmc.kashanu.ac.ir/article_15093_69c2d9a26c71db3e788dad505b39bd47.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
1
2017
03
01
The Topological Indices of some Dendrimer Graph
25
35
EN
M.
R.
Darafsheh
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
M.
Namdari
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
S.
Shokrolahi
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
shokrolahisara@yahoo.com
10.22052/ijmc.2017.15413
In this paper the Wiener and hyper Wiener index of two kinds of dendrimer graphs are determined. Using the Wiener index formula, the Szeged, Schultz, PI and Gutman indices of these graphs are also determined.
Topological index,Dendrimer,Wiener index,Hyper Wiener index
http://ijmc.kashanu.ac.ir/article_15413.html
http://ijmc.kashanu.ac.ir/article_15413_409103bb75ca603e8d9761bff25c9f9d.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
1
2017
03
01
On the Multiplicative Zagreb Indices of Bucket Recursive Trees
37
45
EN
R.
Kazemi
Imam Khomeini international university
r.kazemi@sci.ikiu.ac.ir
10.22052/ijmc.2017.15385
Bucket recursive trees are an interesting and natural generalization of ordinary recursive trees and have a connection to mathematical chemistry. In this paper, we give the lower and upper bounds for the moment generating function and moments of the multiplicative Zagreb indices in a randomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$. Also, we consider the ratio of the multiplicative Zagreb indices for different values of $n$ and $b$. All our results reduce to the ordinary recursive trees for $b=1$.
Bucket recursive trees,Multiplicative Zagreb index,Moment generating function,Moments
http://ijmc.kashanu.ac.ir/article_15385.html
http://ijmc.kashanu.ac.ir/article_15385_a531d26c2c53b9e69340e3275863a39d.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
1
2017
03
01
The Conditions of the Violations of Le Chatlier’s Principle in Gas Reactions at Constant T and P
47
52
EN
M.
Torabi Rad
University of Qom, Qom, Iran
morteza.0mtr0@yahoo.com
A.
Abbasi
University of Qom, Qom, Iran
a.abbasi@qom.ac.ir
10.22052/ijmc.2016.40877
Le Chatelier's principle is used as a very simple way to predict the effect of a change in conditions on a chemical equilibrium. . However, several studies have reported the violation of this principle, still there is no reported simple mathematical equation to express the exact condition of violation in the gas phase reactions. In this article, we derived a simple equation for the violation of Le Chatelier's principle for the ideal gas reactions at the constant temperature and pressure.
Violation of Le Chatelier,Principle gas reaction,Mixture,Chemical equilibria,Chemical potential moderation
http://ijmc.kashanu.ac.ir/article_40877.html
http://ijmc.kashanu.ac.ir/article_40877_16bdbaff387a8d0a5a4560717fd626f1.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
1
2017
03
01
Neighbourly Irregular Derived Graphs
53
60
EN
B.
Basavanagoud
KARNATAK UNIVERSITY DHARWAD
b.basavanagoud@gmail.com
S.
Patil
Karnatak University
shreekantpatil949@gmail.com
V. R.
Desai
Karnatak University
veenardesai6f@gmail.com
M.
Tavakoli
Ferdowsi University of Mashhad
m_tavakoli@um.ac.ir
A. R.
Ashrafi
University of Kashan
ashrafi@kashanu.ac.ir
10.22052/ijmc.2016.40878
A connected graph G is said to be neighbourly irregular graph if no two adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.
Neighbourly irregular,Derived graphs,Product graphs
http://ijmc.kashanu.ac.ir/article_40878.html
http://ijmc.kashanu.ac.ir/article_40878_6696d4ef694484d8cbd24a2e135f2db7.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
1
2017
03
01
Splice Graphs and their Vertex-Degree-Based Invariants
61
70
EN
M.
Azari
Islamic Azad University
mahdie.azari@gmail.com
F.
Falahati-Nezhad
Safadasht Branch, Islamic Azad University
farzanehfalahati_n@yahoo.com
10.22052/ijmc.2017.42671
Let G_1 and G_2 be simple connected graphs with disjoint vertex sets V(G_1) and V(G_2), respectively. For given vertices a_1in V(G_1) and a_2in V(G_2), a splice of G_1 and G_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the union of G_1 and G_2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.
Vertex degree,Graph invariant,Splice
http://ijmc.kashanu.ac.ir/article_42671.html
http://ijmc.kashanu.ac.ir/article_42671_ee6308a68005ada646980828d47bfe6d.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
1
2017
03
01
An Upper Bound on the First Zagreb Index in Trees
71
82
EN
R.
Rasi
Azarbaijan Shahid Madani University, Tabriz, Iran
S.
M.
Sheikholeslami
Azarbaijan Shahid Madani University, Tabriz, Iran
A.
Behmaram
Institute for Research in Fundamental Sciences, Tehran, Iran
behmarammath@gmail.com
10.22052/ijmc.2017.42995
In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.
First Zagreb index,First Zagreb coindex,Tree,Chemical tree
http://ijmc.kashanu.ac.ir/article_42995.html
http://ijmc.kashanu.ac.ir/article_42995_ffcfc35832452f53e30dde47f51eb517.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
8
1
2017
03
01
Distance-Based Topological Indices and Double graph
83
91
EN
M.
K.
Jamil
ABDUS SALAM SCHOOL OF MATHEMATICAL SCIENCES, GOVERNMENT COLLEGE UNIVERSITY, LAHORE, PAKISTAN.
m.kamran.sms@gmail.com
10.22052/ijmc.2017.43073
Let $G$ be a connected graph, and let $D[G]$ denote the double graph of $G$. In this paper, we first derive closed-form formulas for different distance based topological indices for $D[G]$ in terms of that of $G$. Finally, as illustration examples, for several special kind of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for some distance based topological indices.
Wiener index,Harary index,Double graph
http://ijmc.kashanu.ac.ir/article_43073.html
http://ijmc.kashanu.ac.ir/article_43073_2d77910a1fe8582c483e43f4ec4579b4.pdf