2017
8
1
0
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Stirling Numbers and Generalized Zagreb Indices
2
2
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.
1

1
5


T.
Doslic
1Department of Mathematics, Faculty of Civil Engineering, University of Zagreb,
1Department of Mathematics, Faculty of Civil
Croatia
doslic@grad.hr


S.
Sedghi
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshar, Iran
Department of Mathematics, Qaemshahr Branch,
I R Iran
sedghi_gh@yahoo.com


N.
Shobe
Department of Mathematics, Babol Branch,
Islamic Azad
University, Babol, Iran
Department of Mathematics, Babol Branch,
I R Iran
nabi_shobe@yahoo.com
Simple Graph
Zagreb index
Stirling number
Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications
2
2
ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n1)x^(n1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^nm(G,1)x^(n2) + ... where m(G,k) is the number of kmatchings in G. In this paper, we determine the relationship between 2kth coefficient of characteristic polynomial, a_(2k), and kth coefficient of matching polynomial, (1)^km(G, k), in a regular graph. In the rest of this paper, we apply these relations for finding 5,6matchings of fullerene graphs.
1

7
23


F.
Taghvaee
University of Kashan
University of Kashan
I R Iran
taghvaei19@yahoo.com


G.
FathTabar
University of Kashan
University of Kashan
I R Iran
fathtabar@kashanu.ac.ir
Characteristic polynomial
Matching polynomial
Fullerene graph
The Topological Indices of some Dendrimer Graph
2
2
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.
1

25
35


M.
Darafsheh
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran
School of Mathematics, Statistics and Computer
I R Iran


M.
Namdari
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mathematics, Shahid Chamran
I R Iran


S.
Shokrolahi
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
Department of Mathematics, Shahid Chamran
I R Iran
shokrolahisara@yahoo.com
Topological index
Dendrimer
Wiener index
Hyper Wiener index
On the Multiplicative Zagreb Indices of Bucket Recursive Trees
2
2
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 $b=1$.
1

37
45


R.
Kazemi
Imam Khomeini international university
Imam Khomeini international university
I R Iran
r.kazemi@sci.ikiu.ac.ir
Bucket recursive trees
Multiplicative Zagreb index
Moment generating function
Moments
The Conditions of the Violations of Le Chatlier’s Principle in Gas Reactions at Constant T and P
2
2
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.
1

47
52


M.
Torabi Rad
University of Qom, Qom, Iran
University of Qom, Qom, Iran
I R Iran
morteza.0mtr0@yahoo.com


A.
Abbasi
University of Qom, Qom, Iran
University of Qom, Qom, Iran
I R Iran
a.abbasi@qom.ac.ir
Violation of Le Chatelier
Principle gas reaction
Mixture
Chemical equilibria
Chemical potential moderation
Neighbourly Irregular Derived Graphs
2
2
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 semitotalpoint graph, k^{tℎ} semitotalpoint graph, semitotalline graph, paraline graph, quasitotal graph and quasivertextotal graph and also neighbourly irregular of some graph products.
1

53
60


B.
Basavanagoud
KARNATAK UNIVERSITY DHARWAD
KARNATAK UNIVERSITY DHARWAD
India
b.basavanagoud@gmail.com


S.
Patil
Karnatak University
Karnatak University
India
shreekantpatil949@gmail.com


V. R.
Desai
Karnatak University
Karnatak University
India
veenardesai6f@gmail.com


M.
Tavakoli
Ferdowsi University of Mashhad
Ferdowsi University of Mashhad
I R Iran
m_tavakoli@um.ac.ir


A. R.
Ashrafi
University of Kashan
University of Kashan
I R Iran
ashrafi@kashanu.ac.ir
Neighbourly irregular
Derived graphs
Product graphs
Splice Graphs and their VertexDegreeBased Invariants
2
2
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 vertexdegreebased graph invariants of splice of graphs.
1

61
70


M.
Azari
Islamic Azad University
Islamic Azad University
I R Iran
mahdie.azari@gmail.com


F.
FalahatiNezhad
Safadasht Branch, Islamic Azad University
Safadasht Branch, Islamic Azad University
I R Iran
farzanehfalahati_n@yahoo.com
Vertex degree
Graph invariant
Splice
An Upper Bound on the First Zagreb Index in Trees
2
2
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.
1

71
82


R.
Rasi
Azarbaijan Shahid Madani University, Tabriz, Iran
Azarbaijan Shahid Madani University, Tabriz,
I R Iran


S.
Sheikholeslami
Azarbaijan Shahid Madani University, Tabriz, Iran
Azarbaijan Shahid Madani University, Tabriz,
I R Iran


A.
Behmaram
Institute for Research in Fundamental Sciences, Tehran, Iran
Institute for Research in Fundamental Sciences,
I R Iran
behmarammath@gmail.com
First Zagreb index
First Zagreb coindex
Tree
Chemical tree
DistanceBased Topological Indices and Double graph
2
2
Let $G$ be a connected graph, and let $D[G]$ denote the double graph of $G$. In this paper, we first derive closedform 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.
1

83
91


M.
Jamil
ABDUS SALAM SCHOOL OF MATHEMATICAL SCIENCES, GOVERNMENT COLLEGE UNIVERSITY, LAHORE, PAKISTAN.
ABDUS SALAM SCHOOL OF MATHEMATICAL SCIENCES,
Pakistan
m.kamran.sms@gmail.com
Wiener index
Harary index
Double graph