Mathematical Chemistry Works of Dragos Cvetkovic
Ivan
Gutman
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
author
text
article
2019
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
129
136
https://mir.kashanu.ac.ir/article_95507_bbf21ebf318b0d63b6a7ed64364739ab.pdf
dx.doi.org/10.22052/mir.2019.204819.1168
Seidel Integral Complete Split Graphs
Pavel
Hic
Faculty of Education, Trnava University, Trnava, Slovakia
author
Milan
Pokorny
Faculty of Education, Trnava University, Trnava, Slovakia
author
Dragan
Stevanovic
Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia
author
text
article
2019
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
137
150
https://mir.kashanu.ac.ir/article_96006_a1c746b4ddcdc566dcd6fa5e65f3851b.pdf
dx.doi.org/10.22052/mir.2019.194302.1156
Oboudi-Type Bounds for Graph Energy
Ivan
Gutman
Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia
author
text
article
2019
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
151
155
https://mir.kashanu.ac.ir/article_96938_7a344e0905c77f7e7c5531dd406edc2c.pdf
dx.doi.org/10.22052/mir.2019.207442.1172
A Study of PageRank in Undirected Graphs
Abdollah
Lotfi
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
author
Modjtaba
Ghorbani
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
author
Hamid
Mesgarani
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, Iran
author
text
article
2019
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
157
169
https://mir.kashanu.ac.ir/article_100994_4a176ba385e4ccacb68137f1ffe36250.pdf
dx.doi.org/10.22052/mir.2018.125190.1097
Note on the Sum of Powers of Normalized Signless Laplacian Eigenvalues of Graphs
Ş. Burcu
Bozkurt Altındağ
Konya, Turkey
author
text
article
2019
eng
In this paper, for a connected graph G and a real α≠0, we define a new graph invariant σα(G)-as the sum of the alphath powers of the normalized signless Laplacian eigenvalues of G. Note that σ1/2(G) is equal to Randic (normalized) incidence energy which have been recently studied in the literature [5, 15]. We present some bounds on σα(G) (α ≠ 0, 1) and also consider the special case α = 1/2.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
171
182
https://mir.kashanu.ac.ir/article_101587_6d3f9f9d05078067f97d041c27644362.pdf
dx.doi.org/10.22052/mir.2019.208991.1180
The Fourth and Fifth Laplacian Coefficients of some Rooted Trees
Mahsa
Arabzadeh
Department of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. Iran
author
Gholam-Hossein
Fath-Tabar
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan,
Kashan, I. R. Iran
author
Hamid
Rasoli
Department of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. Iran
author
Abolfazl
Tehranian
Department of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. Iran
author
text
article
2019
eng
Abstract. The Laplacian characteristic polynomial of an n-vertex graph G has the form f(G,x) = xn+∑lixn-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).
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
183
192
https://mir.kashanu.ac.ir/article_101588_f54ef31c99328589cc826b00c2bd8846.pdf
dx.doi.org/10.22052/mir.2020.207378.1173
A Multiplicative Version of Forgotten Topological Index
Asghar
Yousefi
Department of Mathematics, Science and Research Branch, Islamic Azad University,
Tehran, Iran
author
Ali
Iranmanesh
Department of Mathematics, Tarbiat Modares University,
Tehran, Iran
author
Andrey
Dobrynin
Sobolev Institute of Mathematics,
Siberian Branch of the Russian Academy of Sciences,
Novosibirsk, Russia
author
Abolfazl
Tehranian
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
author
text
article
2019
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
193
211
https://mir.kashanu.ac.ir/article_102000_e2b2c1124183c3b89ccf0bc81f103cf6.pdf
dx.doi.org/10.22052/mir.2019.176557.1126
On the Configurations with n Points and Two Distances
Ali Asghar
Rezaei
Department of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
Kashan, I. R. Iran
author
text
article
2019
eng
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).
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
213
225
https://mir.kashanu.ac.ir/article_45816_fa687f17a0883ef1c1290ad251cdd442.pdf
dx.doi.org/10.22052/mir.2017.81496.1056
Trees with Extreme Values of Second Zagreb Index and Coindex
Reza
Rasi
Department of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. Iran
author
Seyed Mahmoud
Sheikholeslami
Department of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. Iran
author
Afshin
Behmaram
Faculty of Mathematical Sciences,
University of Tabriz,
Tabriz, I. R. Iran
author
text
article
2019
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
227
238
https://mir.kashanu.ac.ir/article_64769_94f1d4167b1f10a85ce4b7a462e66070.pdf
dx.doi.org/10.22052/mir.2018.130441.1100
Distinguishing Number and Distinguishing Index of the Join of Two Graphs
Saeid
Alikhani
Department of Mathematics, Yazd University, Yazd, Iran
author
Samaneh
Soltani
Department of Mathematics, Yazd University, Yazd, Iran
author
text
article
2019
eng
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 Gk 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 Gk has the distinguishing index 2, except D'(K2+K2)=3.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
239
251
https://mir.kashanu.ac.ir/article_102109_ff92223a27f0fd1dfbcd2f75fc2bc091.pdf
dx.doi.org/10.22052/mir.2020.133523.1102
Probabilistic Properties of F-indices of Trees
Hadis
Morovati
Department of Statistics,
Imam Khomeini International University,
Qazvin, I. R. Iran
author
Ramin
Kazemi
Department of Statistics,
Imam Khomeini International University,
Qazvin, I. R. Iran
author
Akram
Kohansal
Department of Statistics,
Imam Khomeini International University,
Qazvin, I. R. Iran
author
text
article
2019
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
253
261
https://mir.kashanu.ac.ir/article_102110_03ce4c5cdfca7c2b30cafd5a8b6251ba.pdf
dx.doi.org/10.22052/mir.2019.183327.1130
Classification of Bounded Travelling Wave Solutions of the General Burgers-Boussinesq Equation
Rasool
Kazemi
Department of Pure Mathematics,
University of Kashan,
Kashan, I. R. Iran
author
Masoud
Mossadeghi
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 84156-83111
author
text
article
2019
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
263
279
https://mir.kashanu.ac.ir/article_33673_c46440a9ce390b0837c9ce8d88d78e80.pdf
dx.doi.org/10.22052/mir.2016.33673
Graph Invariants of Deleted Lexicographic Product of Graphs
Bahare
Akhavan Mahdavi
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. Iran
author
Mostafa
Tavakoli
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. Iran
author
Freydoon
Rahbarnia
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. Iran
author
text
article
2019
eng
The deleted lexicographic product G[H]-nG of graphs G and H is a graph with vertex set V(G)×V(H) and u=(u1, v1) is adjacent with v=(u2, v2) whenever (u1=u2 and v1 is adjacent with v2) or (v1 ≠ v2 and u1 is adjacent with u2). 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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
281
291
https://mir.kashanu.ac.ir/article_102486_8728c06bbd29a7f7c9f2daefaaa2fa55.pdf
dx.doi.org/10.22052/mir.2019.176548.1125
Best Proximity Point Theorems for Ciric Type G-Contractions in Metric Spaces with a Graph
Kamal
Fallahi
Department of Mathematics, Payam Noor University, Tehran, Iran
author
Mohammad
Hamidi
Department of Mathematics, Payam Noor University, Tehran, Iran
author
text
article
2019
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
293
304
https://mir.kashanu.ac.ir/article_102487_bffa611422018a74ee8545663dd0461f.pdf
dx.doi.org/10.22052/mir.2019.187067.1135
k-Intersection Graph of a Finite Set
Fahimeh
Esmaeeli
Department of Pure Mathematics,
Ferdowsi University of Mashhad,
Mashhad, I. R. Iran
author
Ahmad
Erfanian
Department of Pure Mathematics and The Center of Excellence in Analysis on
Algebraic Structures,
Ferdowsi University of Mashhad,
Mashhad, I. R. Iran
author
Farzaneh
Mansoori
Department of Pure Mathematics,
Ferdowsi University of Mashhad, International Campus
Mashhad, I. R. Iran
author
text
article
2019
eng
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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
305
317
https://mir.kashanu.ac.ir/article_102613_b205b739f72772023b0d554c0ed5cdc2.pdf
dx.doi.org/10.22052/mir.2020.208185.1178
On Eigenvalues of Permutation Graphs
Sima
Saadat-Akhtar
Department of Mathematics,
Faculty of Basic Sciences,
Islamic Azad University,
Central Tehran Branch, Tehran, Iran
author
Shervin
Sahebi
Department of Mathematics,
Faculty of Basic Sciences,
Islamic Azad University,
Central Tehran Branch, Tehran, Iran
author
text
article
2019
eng
Let λ1(G), λ2(G),..., λs(G) be the distinct eigenvalues of G with multiplicities t1, t2,..., ts, respectively. The multiset {λ1(G)t1, λ2(G)t2,..., λs(G)ts} 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.
Mathematics Interdisciplinary Research
University of Kashan
2538-3639
4
v.
2
no.
2019
319
325
https://mir.kashanu.ac.ir/article_102948_a93fee635635058ad0063521ba55abff.pdf
dx.doi.org/10.22052/mir.2020.213088.1189