University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
Mathematical Chemistry Works of Dragos Cvetkovic
129
136
EN
Ivan
Gutman
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
gutman@kg.ac.rs
10.22052/mir.2019.204819.1168
In addition to his countless contributions to spectral graph theory, some works of Dragos Cvetkovic are concerned with chemical problems. These are briefly outlined, with emphasis on his collaboration with the present author.
Spectral graph theory,Mhemical graph theory,molecular graph,Huckel molecular orbital theory
https://mir.kashanu.ac.ir/article_95507.html
https://mir.kashanu.ac.ir/article_95507_bbf21ebf318b0d63b6a7ed64364739ab.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
Seidel Integral Complete Split Graphs
137
150
EN
Pavel
Hic
Faculty of Education, Trnava University, Trnava, Slovakia
phic@truni.sk
Milan
Pokorny
Faculty of Education, Trnava University, Trnava, Slovakia
mpokorny@truni.sk
Dragan
Stevanovic
Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia
dragance106@yahoo.com
10.22052/mir.2019.194302.1156
In the paper we consider a generalized join operation, that is, the H-join on graphs where H is an arbitrary graph. In terms of Seidel matrix of graphs we determine the Seidel spectrum of the graphs obtained by this operation on regular graphs. Some additional consequences regarding S-integral complete split graphs are also obtained, which allows to exhibit many infinite families of Seidel integral complete split graphs.
Seidel spectrum,Seidel integral graph,H-join of graphs,complete split graph
https://mir.kashanu.ac.ir/article_96006.html
https://mir.kashanu.ac.ir/article_96006_a1c746b4ddcdc566dcd6fa5e65f3851b.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
Oboudi-Type Bounds for Graph Energy
151
155
EN
Ivan
Gutman
Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia
gutman@kg.ac.rs
10.22052/mir.2019.207442.1172
The graph energy is the sum of absolute values of the eigenvalues of the (0, 1)-adjacency matrix. Oboudi recently obtained lower bounds for graph energy, depending on the largest and smallest graph eigenvalue. In this paper, a few more Oboudi-type bounds are deduced.
Spectral graph theory,Spectrum (of graph),Graph energy,energy (of graph),Oboudi-type bounds
https://mir.kashanu.ac.ir/article_96938.html
https://mir.kashanu.ac.ir/article_96938_7a344e0905c77f7e7c5531dd406edc2c.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
A Study of PageRank in Undirected Graphs
157
169
EN
Abdollah
Lotfi
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
math.a.lotfi@gmail.com
Modjtaba
Ghorbani
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
ghorbani30@gmail.com
Hamid
Mesgarani
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
hmesgarani@srttu.edu
10.22052/mir.2018.125190.1097
The PageRank (PR) algorithm is the base of Google search engine. In this paper, we study the PageRank sequence for undirected graphs of order six by PR vector. Then, we provide an ordering for graphs by variance of PR vector which it’s variation is proportional with variance of degree sequence. Finally, we introduce a relation between domination number and PR-variance of graphs.
PageRank algorithm,google matrix,Domination number,isomorphism
https://mir.kashanu.ac.ir/article_100994.html
https://mir.kashanu.ac.ir/article_100994_4a176ba385e4ccacb68137f1ffe36250.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
Note on the Sum of Powers of Normalized Signless Laplacian Eigenvalues of Graphs
171
182
EN
Ş. Burcu
Bozkurt Altındağ
0000-0001-9727-6107
Konya, Turkey
srf_burcu_bozkurt@hotmail.com
10.22052/mir.2019.208991.1180
In this paper, for a connected graph G and a real α≠0, we define a new graph invariant σ<sub>α</sub>(G)-as the sum of the alphath powers of the normalized signless Laplacian eigenvalues of G. Note that σ<sub>1/2</sub>(G) is equal to Randic (normalized) incidence energy which have been recently studied in the literature [5, 15]. We present some bounds on σ<sub>α</sub>(G) (α ≠ 0, 1) and also consider the special case α = 1/2.
Normalized signless Laplacian eigenvalues,Randic (normalized) incidence energy,Bound
https://mir.kashanu.ac.ir/article_101587.html
https://mir.kashanu.ac.ir/article_101587_6d3f9f9d05078067f97d041c27644362.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
The Fourth and Fifth Laplacian Coefficients of some Rooted Trees
183
192
EN
Mahsa
Arabzadeh
Department of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. Iran
mahsa.arabzade1177@gmail.com
Gholam-Hossein
Fath-Tabar
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan,
Kashan, I. R. Iran
fathtabar@kashanu.ac.ir
Hamid
Rasoli
Department of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. Iran
hrasouli@srbiau.ac.ir
Abolfazl
Tehranian
Department of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. Iran
tehranian@srbiau.ac.ir
10.22052/mir.2020.207378.1173
Abstract. The Laplacian characteristic polynomial of an n-vertex graph G has the form f(G,x) = x<sup>n</sup>+∑l<sub>ix</sub><sup>n</sup>-i. In this paper, the fourth and fifth coefficient of f(G,x), will be investigated, where G is a T(k,t) tree in which a rooted tree with degree sequence k,k,...,k,1,1,...,1 is denoted by T(k,t).
Graph,Eigenvalue,Laplacian matrix,Laplacian coefficient
https://mir.kashanu.ac.ir/article_101588.html
https://mir.kashanu.ac.ir/article_101588_f54ef31c99328589cc826b00c2bd8846.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
A Multiplicative Version of Forgotten Topological Index
193
211
EN
Asghar
Yousefi
Department of Mathematics, Science and Research Branch, Islamic Azad University,
Tehran, Iran
naser.yosefi53@yahoo.com
Ali
Iranmanesh
Department of Mathematics, Tarbiat Modares University,
Tehran, Iran
iranmana@yahoo.com
Andrey
Dobrynin
Sobolev Institute of Mathematics,
Siberian Branch of the Russian Academy of Sciences,
Novosibirsk, Russia
dobr@math.nsc.ru
Abolfazl
Tehranian
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
tehranian@srbiau.ac.ir
10.22052/mir.2019.176557.1126
In this paper, we present upper bounds for the multiplicative forgotten topological index of several graph operations such as sum, Cartesian product, corona product, composition, strong product, disjunction and symmetric difference in terms of the F–index and the first Zagreb index of their components. Also, we give explicit formulas for this new graph invariant under two graph operations such as union and Tensor product. Moreover, we obtain the expressions for this new graph invariant of subdivision graphs and vertex – semitotal graphs. Finally, we compare the discriminating ability of indices.
topological index,multiplicative forgotten topological index,Graph operations,subdivision graphs,vertex – semitotal graphs
https://mir.kashanu.ac.ir/article_102000.html
https://mir.kashanu.ac.ir/article_102000_e2b2c1124183c3b89ccf0bc81f103cf6.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
On the Configurations with n Points and Two Distances
213
225
EN
Ali Asghar
Rezaei
Department of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
Kashan, I. R. Iran
a_rezaei@kashanu.ac.ir
10.22052/mir.2017.81496.1056
In this paper we investigate the geometric structures of M(n, 2) containing n points in R^3 having two distinct distances. We will show that up to pseudo-equivalence there are 5 constructible models for M(4, 2) and 17 constructible models for M(5, 2).
Constructible models,distinct distances,isomorphic graphs,pseudo-equivalent models
https://mir.kashanu.ac.ir/article_45816.html
https://mir.kashanu.ac.ir/article_45816_fa687f17a0883ef1c1290ad251cdd442.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
Trees with Extreme Values of Second Zagreb Index and Coindex
227
238
EN
Reza
Rasi
Department of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. Iran
r.rasi@azaruniv.ac.ir
Seyed Mahmoud
Sheikholeslami
Department of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. Iran
sm.sheikholeslami@azaruniv.edu
Afshin
Behmaram
Faculty of Mathematical Sciences,
University of Tabriz,
Tabriz, I. R. Iran
behmarammath@gmail.com
10.22052/mir.2018.130441.1100
In this paper we present a generalization of the aforementioned bound for all trees in terms of the order and maximum degree. We also give a lower bound on the second Zagreb coindex of trees.
Zagreb index,second Zagreb index,second Zagreb coindex,Tree
https://mir.kashanu.ac.ir/article_64769.html
https://mir.kashanu.ac.ir/article_64769_94f1d4167b1f10a85ce4b7a462e66070.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
Distinguishing Number and Distinguishing Index of the Join of Two Graphs
239
251
EN
Saeid
Alikhani
Department of Mathematics, Yazd University, Yazd, Iran
alikhani206@gmail.com
Samaneh
Soltani
Department of Mathematics, Yazd University, Yazd, Iran
s.soltani1979@gmail.com
10.22052/mir.2020.133523.1102
The distinguishing number (index) D(G) (D'(G)) of a graph G is the least integer d such that G has an vertex labeling (edge labeling) with d labels that is preserved only by a trivial automorphism. In this paper we study the distinguishing number and the distinguishing index of the join of two graphs G and H, i.e., G+H. We prove that 0≤ D(G+H)-max{D(G),D(H)}≤ z, where z depends on the number of some induced subgraphs generated by some suitable partitions of V(G) and V(H). Let G<sup>k</sup> be the k-th power of G with respect to the join product. We prove that if G is a connected graph of order n ≥ 2, then G<sup>k</sup> has the distinguishing index 2, except D'(K<sub>2</sub>+K<sub>2</sub>)=3.
Distinguishing index,distinguishing number,join
https://mir.kashanu.ac.ir/article_102109.html
https://mir.kashanu.ac.ir/article_102109_ff92223a27f0fd1dfbcd2f75fc2bc091.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
Probabilistic Properties of F-indices of Trees
253
261
EN
Hadis
Morovati
Department of Statistics,
Imam Khomeini International University,
Qazvin, I. R. Iran
rst.kazemi@gmail.com
Ramin
Kazemi
Department of Statistics,
Imam Khomeini International University,
Qazvin, I. R. Iran
r.kazemi@sci.ikiu.ac.ir
Akram
Kohansal
Department of Statistics,
Imam Khomeini International University,
Qazvin, I. R. Iran
kazemi@ikiu.ac.ir
10.22052/mir.2019.183327.1130
The aim of this paper is to introduce some results for the F-index of the tree structures without any information on the exact values of vertex degrees. Three martingales related to the first Zagreb index and F-index are given.
Tree structures,F-indices,martingale
https://mir.kashanu.ac.ir/article_102110.html
https://mir.kashanu.ac.ir/article_102110_03ce4c5cdfca7c2b30cafd5a8b6251ba.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
Classification of Bounded Travelling Wave Solutions of the General Burgers-Boussinesq Equation
263
279
EN
Rasool
Kazemi
Department of Pure Mathematics,
University of Kashan,
Kashan, I. R. Iran
r.kazemi@kashanu.ac.ir
Masoud
Mossadeghi
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 84156-83111
m.mosaddeghi@math.iut.ac.ir
10.22052/mir.2016.33673
By using bifurcation theory of planar dynamical systems, we classify all bounded travelling wave solutions of the general Burgers-Boussinesq equation, and we give their corresponding phase portraits. In different parametric regions, different types of trav- elling wave solutions such as solitary wave solutions, cusp solitary wave solutions, kink(anti kink) wave solutions and periodic wave solutions are simulated. Also in each parameter bifurcation sets, we obtain the exact explicit parametric representation of all travelling wave solutions.
General Burgers-Boussinesq equation,travelling wave solutions,bifurcation theory
https://mir.kashanu.ac.ir/article_33673.html
https://mir.kashanu.ac.ir/article_33673_c46440a9ce390b0837c9ce8d88d78e80.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
Graph Invariants of Deleted Lexicographic Product of Graphs
281
291
EN
Bahare
Akhavan Mahdavi
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. Iran
bahare.akhavan@um.ac.ir
Mostafa
Tavakoli
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. Iran
m_tavakoli@um.ac.ir
Freydoon
Rahbarnia
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. Iran
rahbarnia@um.ac.ir
10.22052/mir.2019.176548.1125
The deleted lexicographic product G[H]-nG of graphs G and H is a graph with vertex set V(G)×V(H) and u=(u<sub>1</sub>, v<sub>1</sub>) is adjacent with v=(u<sub>2</sub>, v<sub>2</sub>) whenever (u<sub>1</sub>=u<sub>2</sub> and v<sub>1</sub> is adjacent with v<sub>2</sub>) or (v<sub>1</sub> ≠ v<sub>2</sub> and u<sub>1</sub> is adjacent with u<sub>2</sub>). In this paper, we compute the exact values of the Wiener, vertex PI and Zagreb indices of deleted lexicographic product of graphs. Applications of our results under some examples are presented.<br />
Deleted lexicographic product,Wiener index,Vertex PI index,Zagreb indices
https://mir.kashanu.ac.ir/article_102486.html
https://mir.kashanu.ac.ir/article_102486_8728c06bbd29a7f7c9f2daefaaa2fa55.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
Best Proximity Point Theorems for Ciric Type G-Contractions in Metric Spaces with a Graph
293
304
EN
Kamal
Fallahi
0000-0003-3400-4424
Department of Mathematics, Payam Noor University, Tehran, Iran
fallahi1361@gmail.com
Mohammad
Hamidi
Department of Mathematics, Payam Noor University, Tehran, Iran
m.hamidi@pnu.ac.ir
10.22052/mir.2019.187067.1135
In this paper, we aim to introduce Ciric type G-contractions using directed graphs in metric spaces and then to investigate the existence and uniqueness of best proximity points for them. We also discuss the main theorem and list some consequences of it.
G-proximal mapping,Ciric type G-contraction,Best proximity point
https://mir.kashanu.ac.ir/article_102487.html
https://mir.kashanu.ac.ir/article_102487_bffa611422018a74ee8545663dd0461f.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
k-Intersection Graph of a Finite Set
305
317
EN
Fahimeh
Esmaeeli
Department of Pure Mathematics,
Ferdowsi University of Mashhad,
Mashhad, I. R. Iran
fahimeh.smaily@gmail.com
Ahmad
Erfanian
0000-0002-9637-1417
Department of Pure Mathematics and The Center of Excellence in Analysis on
Algebraic Structures,
Ferdowsi University of Mashhad,
Mashhad, I. R. Iran
erfanian@um.ac.ir
Farzaneh
Mansoori
Department of Pure Mathematics,
Ferdowsi University of Mashhad, International Campus
Mashhad, I. R. Iran
mansoori.farzaneh@gmail.com
10.22052/mir.2020.208185.1178
For any nonempty set Ω and k-subset Λ, the k-intersection graph, denoted by Γm(Ω,Λ), is an undirected simple graph whose vertices are all m-subsets of Ω and two distinct vertices A and B are adjacent if and only if A∩B ⊈ Λ. In this paper, we determine diameter, girth, some numerical invariants and planarity, Hamiltonian and perfect matching of these graphs. ﬁnally we investigate their adjacency matrices.
intersection graph,k-intersection graph,diameter
https://mir.kashanu.ac.ir/article_102613.html
https://mir.kashanu.ac.ir/article_102613_b205b739f72772023b0d554c0ed5cdc2.pdf
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
4
2
2019
12
01
On Eigenvalues of Permutation Graphs
319
325
EN
Sima
Saadat-Akhtar
Department of Mathematics,
Faculty of Basic Sciences,
Islamic Azad University,
Central Tehran Branch, Tehran, Iran
simasaadatzzz3@gmail.com
Shervin
Sahebi
Department of Mathematics,
Faculty of Basic Sciences,
Islamic Azad University,
Central Tehran Branch, Tehran, Iran
sahebi@iauctb.ac.ir
10.22052/mir.2020.213088.1189
Let λ<sub>1</sub>(G), λ<sub>2</sub>(G),..., λ<sub>s</sub>(G) be the distinct eigenvalues of G with multiplicities t<sub>1</sub>, t<sub>2</sub>,..., t<sub>s</sub>, respectively. The multiset {λ<sub>1</sub>(G)<sup>t<sub>1</sub></sup>, λ<sub>2</sub>(G)<sup>t<sub>2</sub></sup>,..., λ<sub>s</sub>(G)<sup>t<sub>s</sub></sup>} of eigenvalues of A(G) is called the spectrum of G. For two graphs G and H, if their spectrum are the same, then G and H are said to be co-spectral. The aim of this paper is to determine co-spectral permutation graphs with respect to automorphism group of graph G.
Permutation graph,Petersen graph,Automorphism group
https://mir.kashanu.ac.ir/article_102948.html
https://mir.kashanu.ac.ir/article_102948_a93fee635635058ad0063521ba55abff.pdf