eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
129
136
10.22052/mir.2019.204819.1168
95507
Mathematical Chemistry Works of Dragos Cvetkovic
Ivan Gutman
gutman@kg.ac.rs
1
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
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.
http://mir.kashanu.ac.ir/article_95507_bbf21ebf318b0d63b6a7ed64364739ab.pdf
Spectral graph theory
chemical graph theory
molecular graph
Huckel molecular orbital theory
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
137
150
10.22052/mir.2019.194302.1156
96006
Seidel Integral Complete Split Graphs
Pavel Hic
phic@truni.sk
1
Milan Pokorny
mpokorny@truni.sk
2
Dragan Stevanovic
dragance106@yahoo.com
3
Faculty of Education, Trnava University, Trnava, Slovakia
Faculty of Education, Trnava University, Trnava, Slovakia
Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia
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.
http://mir.kashanu.ac.ir/article_96006_a1c746b4ddcdc566dcd6fa5e65f3851b.pdf
Seidel spectrum
Seidel integral graph
H-join of graphs
complete split graph
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
151
155
10.22052/mir.2019.207442.1172
96938
Oboudi-Type Bounds for Graph Energy
Ivan Gutman
gutman@kg.ac.rs
1
Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia
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.
http://mir.kashanu.ac.ir/article_96938_7a344e0905c77f7e7c5531dd406edc2c.pdf
Spectral graph theory
Spectrum (of graph)
Graph energy
energy (of graph)
Oboudi-type bounds
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
157
169
10.22052/mir.2018.125190.1097
100994
A Study of PageRank in Undirected Graphs
Abdollah Lotfi
math.a.lotfi@gmail.com
1
Modjtaba Ghorbani
ghorbani30@gmail.com
2
Hamid Mesgarani
hmesgarani@srttu.edu
3
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
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.
http://mir.kashanu.ac.ir/article_100994_4a176ba385e4ccacb68137f1ffe36250.pdf
PageRank algorithm
google matrix
Domination number
isomorphism
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
171
182
10.22052/mir.2019.208991.1180
101587
Note on the Sum of Powers of Normalized Signless Laplacian Eigenvalues of Graphs
Ş. Burcu Bozkurt Altındağ
srf_burcu_bozkurt@hotmail.com
1
Konya, Turkey
In this paper, for a connected graph G and a real alpha (not equal to) 0, we define a new graph invariant sigma_alpha (G)-as the sum of the alphath powers of the normalized signless Laplacian eigenvalues of G. Note that sigma_1/2 (G) is equal to Randic (normalized) incidence energy which have been recently studied in the literature [5, 15]. We present some bounds on sigma_alpha(G) (alpha (not equal to) 0, 1) and also consider the special case alpha = 1/2.
http://mir.kashanu.ac.ir/article_101587_6d3f9f9d05078067f97d041c27644362.pdf
Normalized signless Laplacian eigenvalues
Randic (normalized) incidence energy
Bound
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
183
192
10.22052/mir.2020.207378.1173
101588
The Fourth and Fifth Laplacian Coefficients of some Rooted Trees
Mahsa Arabzadeh
mahsa.arabzade1177@gmail.com
1
Gholam-Hossein Fath-Tabar
fathtabar@kashanu.ac.ir
2
Hamid Rasoli
hrasouli@srbiau.ac.ir
3
Abolfazl Tehranian
tehranian@srbiau.ac.ir
4
Department of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. Iran
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran
Department of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. Iran
Department of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. Iran
Abstract. The Laplacian characteristic polynomial of an n-vertex graph G has the form f(G,x) = x^n+∑l_ix^n-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).
http://mir.kashanu.ac.ir/article_101588_f54ef31c99328589cc826b00c2bd8846.pdf
Graph
Eigenvalue
Laplacian matrix
Laplacian coefficient
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
193
211
10.22052/mir.2019.176557.1126
102000
A Multiplicative Version of Forgotten Topological Index
Asghar Yousefi
naser.yosefi53@yahoo.com
1
Ali Iranmanesh
iranmana@yahoo.com
2
Andrey Dobrynin
dobr@math.nsc.ru
3
Abolfazl Tehranian
tehranian@srbiau.ac.ir
4
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Mathematics, Tarbiat Modares University, Tehran, Iran
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
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.
http://mir.kashanu.ac.ir/article_102000_e2b2c1124183c3b89ccf0bc81f103cf6.pdf
topological index
multiplicative forgotten topological index
Graph operations
subdivision graphs
vertex – semitotal graphs
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
213
225
10.22052/mir.2017.81496.1056
45816
On the Configurations with n Points and Two Distances
Ali Asghar Rezaei
a_rezaei@kashanu.ac.ir
1
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. Iran
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).
http://mir.kashanu.ac.ir/article_45816_fa687f17a0883ef1c1290ad251cdd442.pdf
Constructible models
distinct distances
isomorphic graphs
pseudo-equivalent models
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
227
238
10.22052/mir.2018.130441.1100
64769
Trees with Extreme Values of Second Zagreb Index and Coindex
Reza Rasi
r.rasi@azaruniv.ac.ir
1
Seyed Mahmoud Sheikholeslami
sm.sheikholeslami@azaruniv.edu
2
Afshin Behmaram
behmarammath@gmail.com
3
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I. R. Iran
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, I. R. Iran
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.
http://mir.kashanu.ac.ir/article_64769_94f1d4167b1f10a85ce4b7a462e66070.pdf
Zagreb index
second Zagreb index
second Zagreb coindex
tree
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
239
251
10.22052/mir.2020.133523.1102
102109
Distinguishing Number and Distinguishing Index of the Join of Two Graphs
Saeid Alikhani
alikhani206@gmail.com
1
Samaneh Soltani
s.soltani1979@gmail.com
2
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
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_2+K_2)=3.
http://mir.kashanu.ac.ir/article_102109_ff92223a27f0fd1dfbcd2f75fc2bc091.pdf
Distinguishing index
distinguishing number
join
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
253
261
10.22052/mir.2019.183327.1130
102110
Probabilistic Properties of F-indices of Trees
Hadis Morovati
rst.kazemi@gmail.com
1
Ramin Kazemi
r.kazemi@sci.ikiu.ac.ir
2
Akram Kohansal
kazemi@ikiu.ac.ir
3
Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran
Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran
Department of Statistics, Imam Khomeini International University, Qazvin, I. R. Iran
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.
http://mir.kashanu.ac.ir/article_102110_03ce4c5cdfca7c2b30cafd5a8b6251ba.pdf
Tree structures
F-indices
martingale
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
263
279
10.22052/mir.2016.33673
33673
Classification of Bounded Travelling Wave Solutions of the General Burgers-Boussinesq Equation
Rasool Kazemi
r.kazemi@kashanu.ac.ir
1
Masoud Mossadeghi
m.mosaddeghi@math.iut.ac.ir
2
Department of Pure Mathematics, University of Kashan, Kashan, I. R. Iran
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 84156-83111
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.
http://mir.kashanu.ac.ir/article_33673_c46440a9ce390b0837c9ce8d88d78e80.pdf
General Burgers-Boussinesq equation
travelling wave solutions
bifurcation theory
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
281
291
10.22052/mir.2019.176548.1125
102486
Graph Invariants of Deleted Lexicographic Product of Graphs
Bahare Akhavan Mahdavi
bahare.akhavan@um.ac.ir
1
Mostafa Tavakoli
m_tavakoli@um.ac.ir
2
Freydoon Rahbarnia
rahbarnia@um.ac.ir
3
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. Iran
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 />
http://mir.kashanu.ac.ir/article_102486_8728c06bbd29a7f7c9f2daefaaa2fa55.pdf
Deleted lexicographic product
Wiener index
Vertex PI index
Zagreb indices
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
293
304
10.22052/mir.2019.187067.1135
102487
Best Proximity Point Theorems for Ciric Type G-Contractions in Metric Spaces with a Graph
Kamal Fallahi
fallahi1361@gmail.com
1
Mohammad Hamidi
m.hamidi@pnu.ac.ir
2
Department of Mathematics, Payam Noor University, Tehran, Iran
Department of Mathematics, Payam Noor University, Tehran, Iran
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.
http://mir.kashanu.ac.ir/article_102487_bffa611422018a74ee8545663dd0461f.pdf
G-proximal mapping
Ciric type G-contraction
Best proximity point
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
305
317
10.22052/mir.2020.208185.1178
102613
k-Intersection Graph of a Finite Set
Fahimeh Esmaeeli
fahimeh.smaily@gmail.com
1
Ahmad Erfanian
erfanian@um.ac.ir
2
Farzaneh Mansoori
mansoori.farzaneh@gmail.com
3
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, I. R. Iran
Department of Pure Mathematics and The Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, I. R. Iran
Department of Pure Mathematics, Ferdowsi University of Mashhad, International Campus Mashhad, I. R. Iran
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.
http://mir.kashanu.ac.ir/article_102613_b205b739f72772023b0d554c0ed5cdc2.pdf
intersection graph
k-intersection graph
diameter
eng
University of Kashan
Mathematics Interdisciplinary Research
2538-3639
2476-4965
2019-12-01
4
2
319
325
10.22052/mir.2020.213088.1189
102948
On Eigenvalues of Permutation Graphs
Sima Saadat-Akhtar
simasaadatzzz3@gmail.com
1
Shervin Sahebi
sahebi@iauctb.ac.ir
2
Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Central Tehran Branch, Tehran, Iran
Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Central Tehran Branch, Tehran, Iran
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.
http://mir.kashanu.ac.ir/article_102948_a93fee635635058ad0063521ba55abff.pdf
Permutation graph
Petersen graph
Automorphism group