eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-03-01
8
1
1
5
10.22052/ijmc.2017.15092
15092
Stirling Numbers and Generalized Zagreb Indices
T. Doslic
doslic@grad.hr
1
S. Sedghi
sedghi_gh@yahoo.com
2
N. Shobe
nabi_shobe@yahoo.com
3
1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb,
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshar, Iran
Department of Mathematics, Babol Branch, Islamic Azad University, Babol, Iran
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.
http://ijmc.kashanu.ac.ir/article_15092_b7bb85d9dbe4ac40d6d223adc42453dd.pdf
Simple Graph
Zagreb index
Stirling number
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-03-01
8
1
7
23
10.22052/ijmc.2017.15093
15093
Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications
F. Taghvaee
taghvaei19@yahoo.com
1
G. Fath-Tabar
fathtabar@kashanu.ac.ir
2
University of Kashan
University of Kashan
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.
http://ijmc.kashanu.ac.ir/article_15093_be5ca1f23c477021c246d4c612236dc6.pdf
Characteristic polynomial
Matching polynomial
Fullerene graph
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-03-01
8
1
25
35
10.22052/ijmc.2017.15413
15413
The Topological Indices of some Dendrimer Graphs
M. Darafsheh
1
M. Namdari
2
S. Shokrolahi
shokrolahisara@yahoo.com
3
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
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.
http://ijmc.kashanu.ac.ir/article_15413_df8b2c0cfc3d418f4b890e723474b4cd.pdf
topological index
Dendrimer
Wiener index
Hyper Wiener index
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-03-01
8
1
37
45
10.22052/ijmc.2017.15385
15385
On the Multiplicative Zagreb Indices of Bucket Recursive Trees
R. Kazemi
r.kazemi@sci.ikiu.ac.ir
1
Imam Khomeini international university
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 $b=1$.
http://ijmc.kashanu.ac.ir/article_15385_09d45a56a3e6e888884635bfc073bf60.pdf
Bucket recursive trees
Multiplicative Zagreb index
Moment generating function
Moments
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-03-01
8
1
47
52
10.22052/ijmc.2016.40877
40877
The Conditions of the Violations of Le Chatlier’s Principle in Gas Reactions at Constant T and P
M. Torabi Rad
morteza.0mtr0@yahoo.com
1
A. Abbasi
a.abbasi@qom.ac.ir
2
University of Qom, Qom, Iran
University of Qom, Qom, Iran
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.
http://ijmc.kashanu.ac.ir/article_40877_8ff2dc0bd3328b97fc4cc4983d8d533a.pdf
Violation of Le Chatelier
Principle gas reaction
Mixture
Chemical equilibria
Chemical potential moderation
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-03-01
8
1
53
60
10.22052/ijmc.2016.40878
40878
Neighbourly Irregular Derived Graphs
B. Basavanagoud
b.basavanagoud@gmail.com
1
S. Patil
shreekantpatil949@gmail.com
2
V. R. Desai
veenardesai6f@gmail.com
3
M. Tavakoli
m_tavakoli@um.ac.ir
4
A. R. Ashrafi
ashrafi@kashanu.ac.ir
5
KARNATAK UNIVERSITY DHARWAD
Karnatak University
Karnatak University
Ferdowsi University of Mashhad
University of Kashan
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.
http://ijmc.kashanu.ac.ir/article_40878_84e728f990f1722c2fdf11f8aec1c6e0.pdf
Neighbourly irregular
Derived graphs
Product graphs
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-03-01
8
1
61
70
10.22052/ijmc.2017.42671
42671
Splice Graphs and their Vertex-Degree-Based Invariants
M. Azari
mahdie.azari@gmail.com
1
F. Falahati-Nezhad
farzanehfalahati_n@yahoo.com
2
Islamic Azad University
Safadasht Branch, Islamic Azad University
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.
http://ijmc.kashanu.ac.ir/article_42671_842a36edd0ad831bf464f22081c22654.pdf
vertex degree
graph invariant
Splice
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-03-01
8
1
71
82
10.22052/ijmc.2017.42995
42995
An Upper Bound on the First Zagreb Index in Trees
R. Rasi
1
S. Sheikholeslami
2
A. Behmaram
behmarammath@gmail.com
3
Azarbaijan Shahid Madani University, Tabriz, Iran
Azarbaijan Shahid Madani University, Tabriz, Iran
Institute for Research in Fundamental Sciences, Tehran, Iran
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.
http://ijmc.kashanu.ac.ir/article_42995_aceaeaa2290cdaa2217a2205d4bda5af.pdf
First Zagreb index
First Zagreb coindex
tree
Chemical tree
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2017-03-01
8
1
83
91
10.22052/ijmc.2017.43073
43073
Distance-Based Topological Indices and Double graph
M. Jamil
m.kamran.sms@gmail.com
1
ABDUS SALAM SCHOOL OF MATHEMATICAL SCIENCES, GOVERNMENT COLLEGE UNIVERSITY, LAHORE, PAKISTAN.
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.
http://ijmc.kashanu.ac.ir/article_43073_1e1bbd86540bb1e1baabd2a8f90bff47.pdf
Wiener index
Harary index
Double graph