Stirling Numbers and Generalized Zagreb Indices
T.
Doslic
1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb,
author
S.
Sedghi
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshar, Iran
author
N.
Shobe
Department of Mathematics, Babol Branch,
Islamic Azad
University, Babol, Iran
author
text
article
2017
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
1
no.
2017
1
5
http://ijmc.kashanu.ac.ir/article_15092_b7bb85d9dbe4ac40d6d223adc42453dd.pdf
dx.doi.org/10.22052/ijmc.2017.15092
Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications
F.
Taghvaee
University of Kashan
author
G.
Fath-Tabar
University of Kashan
author
text
article
2017
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
1
no.
2017
7
23
http://ijmc.kashanu.ac.ir/article_15093_be5ca1f23c477021c246d4c612236dc6.pdf
dx.doi.org/10.22052/ijmc.2017.15093
The Topological Indices of some Dendrimer Graphs
M.
Darafsheh
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
author
M.
Namdari
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
author
S.
Shokrolahi
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
author
text
article
2017
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
1
no.
2017
25
35
http://ijmc.kashanu.ac.ir/article_15413_df8b2c0cfc3d418f4b890e723474b4cd.pdf
dx.doi.org/10.22052/ijmc.2017.15413
On the Multiplicative Zagreb Indices of Bucket Recursive Trees
R.
Kazemi
Imam Khomeini international university
author
text
article
2017
eng
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 $b=1$.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
1
no.
2017
37
45
http://ijmc.kashanu.ac.ir/article_15385_09d45a56a3e6e888884635bfc073bf60.pdf
dx.doi.org/10.22052/ijmc.2017.15385
The Conditions of the Violations of Le Chatlier’s Principle in Gas Reactions at Constant T and P
M.
Torabi Rad
University of Qom, Qom, Iran
author
A.
Abbasi
University of Qom, Qom, Iran
author
text
article
2017
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
1
no.
2017
47
52
http://ijmc.kashanu.ac.ir/article_40877_8ff2dc0bd3328b97fc4cc4983d8d533a.pdf
dx.doi.org/10.22052/ijmc.2016.40877
Neighbourly Irregular Derived Graphs
B.
Basavanagoud
KARNATAK UNIVERSITY DHARWAD
author
S.
Patil
Karnatak University
author
V. R.
Desai
Karnatak University
author
M.
Tavakoli
Ferdowsi University of Mashhad
author
A. R.
Ashrafi
University of Kashan
author
text
article
2017
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
1
no.
2017
53
60
http://ijmc.kashanu.ac.ir/article_40878_84e728f990f1722c2fdf11f8aec1c6e0.pdf
dx.doi.org/10.22052/ijmc.2016.40878
Splice Graphs and their Vertex-Degree-Based Invariants
M.
Azari
Islamic Azad University
author
F.
Falahati-Nezhad
Safadasht Branch, Islamic Azad University
author
text
article
2017
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
1
no.
2017
61
70
http://ijmc.kashanu.ac.ir/article_42671_842a36edd0ad831bf464f22081c22654.pdf
dx.doi.org/10.22052/ijmc.2017.42671
An Upper Bound on the First Zagreb Index in Trees
R.
Rasi
Azarbaijan Shahid Madani University, Tabriz, Iran
author
S.
Sheikholeslami
Azarbaijan Shahid Madani University, Tabriz, Iran
author
A.
Behmaram
Institute for Research in Fundamental Sciences, Tehran, Iran
author
text
article
2017
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
1
no.
2017
71
82
http://ijmc.kashanu.ac.ir/article_42995_aceaeaa2290cdaa2217a2205d4bda5af.pdf
dx.doi.org/10.22052/ijmc.2017.42995
Distance-Based Topological Indices and Double graph
M.
Jamil
ABDUS SALAM SCHOOL OF MATHEMATICAL SCIENCES, GOVERNMENT COLLEGE UNIVERSITY, LAHORE, PAKISTAN.
author
text
article
2017
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
8
v.
1
no.
2017
83
91
http://ijmc.kashanu.ac.ir/article_43073_1e1bbd86540bb1e1baabd2a8f90bff47.pdf
dx.doi.org/10.22052/ijmc.2017.43073