University of KashanMathematics Interdisciplinary Research2538-36394220191201Mathematical Chemistry Works of Dragos Cvetkovic1291369550710.22052/mir.2019.204819.1168ENIvan GutmanFaculty of Science, University of Kragujevac, Kragujevac, SerbiaJournal Article20191006In 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.https://mir.kashanu.ac.ir/article_95507_bbf21ebf318b0d63b6a7ed64364739ab.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201Seidel Integral Complete Split Graphs1371509600610.22052/mir.2019.194302.1156ENPavel HicFaculty of Education, Trnava University, Trnava, SlovakiaMilan PokornyFaculty of Education, Trnava University, Trnava, SlovakiaDragan StevanovicMathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, SerbiaJournal Article20190714In 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.https://mir.kashanu.ac.ir/article_96006_a1c746b4ddcdc566dcd6fa5e65f3851b.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201Oboudi-Type Bounds for Graph Energy1511559693810.22052/mir.2019.207442.1172ENIvan GutmanFaculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, SerbiaJournal Article20191103The 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.https://mir.kashanu.ac.ir/article_96938_7a344e0905c77f7e7c5531dd406edc2c.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201A Study of PageRank in Undirected Graphs15716910099410.22052/mir.2018.125190.1097ENAbdollah LotfiDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, IranModjtaba GhorbaniDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, IranHamid MesgaraniDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, IranJournal Article20180316The 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.https://mir.kashanu.ac.ir/article_100994_4a176ba385e4ccacb68137f1ffe36250.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201Note on the Sum of Powers of Normalized Signless Laplacian Eigenvalues of Graphs17118210158710.22052/mir.2019.208991.1180ENŞ. Burcu Bozkurt AltındağKonya, Turkey0000-0001-9727-6107Journal Article20191118In 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.https://mir.kashanu.ac.ir/article_101587_6d3f9f9d05078067f97d041c27644362.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201The Fourth and Fifth Laplacian Coefficients of some Rooted Trees18319210158810.22052/mir.2020.207378.1173ENMahsa ArabzadehDepartment of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. IranGholam-Hossein Fath-TabarDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan,
Kashan, I. R. IranHamid RasoliDepartment of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. IranAbolfazl TehranianDepartment of Mathematics, Islamic Azad University, Science and Researcher Branch Tehran, I. R. IranJournal Article20191103Abstract. 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).https://mir.kashanu.ac.ir/article_101588_f54ef31c99328589cc826b00c2bd8846.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201A Multiplicative Version of Forgotten Topological Index19321110200010.22052/mir.2019.176557.1126ENAsghar YousefiDepartment of Mathematics, Science and Research Branch, Islamic Azad University,
Tehran, IranAli IranmaneshDepartment of Mathematics, Tarbiat Modares University,
Tehran, IranAndrey DobryninSobolev Institute of Mathematics,
Siberian Branch of the Russian Academy of Sciences,
Novosibirsk, RussiaAbolfazl TehranianDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranJournal Article20190318In 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.https://mir.kashanu.ac.ir/article_102000_e2b2c1124183c3b89ccf0bc81f103cf6.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201On the Configurations with n Points and Two Distances2132254581610.22052/mir.2017.81496.1056ENAli Asghar RezaeiDepartment of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan,
Kashan, I. R. IranJournal Article20170407In 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).https://mir.kashanu.ac.ir/article_45816_fa687f17a0883ef1c1290ad251cdd442.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201Trees with Extreme Values of Second Zagreb Index and Coindex2272386476910.22052/mir.2018.130441.1100ENReza RasiDepartment of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. IranSeyed Mahmoud SheikholeslamiDepartment of Mathematics,
Azarbaijan Shahid Madani University,
Tabriz, I. R. IranAfshin BehmaramFaculty of Mathematical Sciences,
University of Tabriz,
Tabriz, I. R. IranJournal Article20180511In 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.https://mir.kashanu.ac.ir/article_64769_94f1d4167b1f10a85ce4b7a462e66070.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201Distinguishing Number and Distinguishing Index of the Join of Two Graphs23925110210910.22052/mir.2020.133523.1102ENSaeid AlikhaniDepartment of Mathematics, Yazd University, Yazd, IranSamaneh SoltaniDepartment of Mathematics, Yazd University, Yazd, IranJournal Article20180526The 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.https://mir.kashanu.ac.ir/article_102109_ff92223a27f0fd1dfbcd2f75fc2bc091.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201Probabilistic Properties of F-indices of Trees25326110211010.22052/mir.2019.183327.1130ENHadis MorovatiDepartment of Statistics,
Imam Khomeini International University,
Qazvin, I. R. IranRamin KazemiDepartment of Statistics,
Imam Khomeini International University,
Qazvin, I. R. IranAkram KohansalDepartment of Statistics,
Imam Khomeini International University,
Qazvin, I. R. IranJournal Article20190427The 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.https://mir.kashanu.ac.ir/article_102110_03ce4c5cdfca7c2b30cafd5a8b6251ba.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201Classification of Bounded Travelling Wave Solutions of the General Burgers-Boussinesq Equation2632793367310.22052/mir.2016.33673ENRasool KazemiDepartment of Pure Mathematics,
University of Kashan,
Kashan, I. R. IranMasoud MossadeghiDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran, 84156-83111Journal Article20160423By 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.https://mir.kashanu.ac.ir/article_33673_c46440a9ce390b0837c9ce8d88d78e80.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201Graph Invariants of Deleted Lexicographic Product of Graphs28129110248610.22052/mir.2019.176548.1125ENBahare Akhavan MahdaviDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. IranMostafa TavakoliDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. Iran0000-0002-3315-1759Freydoon RahbarniaDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, I. R. IranJournal Article20190318The 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 /> https://mir.kashanu.ac.ir/article_102486_8728c06bbd29a7f7c9f2daefaaa2fa55.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201Best Proximity Point Theorems for Ciric Type G-Contractions in Metric Spaces with a Graph29330410248710.22052/mir.2019.187067.1135ENKamal FallahiDepartment of Mathematics, Payam Noor University, Tehran, Iran0000-0003-3400-4424Mohammad HamidiDepartment of Mathematics, Payam Noor University, Tehran, IranJournal Article20190523In 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.https://mir.kashanu.ac.ir/article_102487_bffa611422018a74ee8545663dd0461f.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201k-Intersection Graph of a Finite Set30531710261310.22052/mir.2020.208185.1178ENFahimeh EsmaeeliDepartment of Pure Mathematics,
Ferdowsi University of Mashhad,
Mashhad, I. R. IranAhmad ErfanianDepartment of Pure Mathematics and The Center of Excellence in Analysis on
Algebraic Structures,
Ferdowsi University of Mashhad,
Mashhad, I. R. Iran0000-0002-9637-1417Farzaneh MansooriDepartment of Pure Mathematics,
Ferdowsi University of Mashhad, International Campus
Mashhad, I. R. IranJournal Article20191109For 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.https://mir.kashanu.ac.ir/article_102613_b205b739f72772023b0d554c0ed5cdc2.pdfUniversity of KashanMathematics Interdisciplinary Research2538-36394220191201On Eigenvalues of Permutation Graphs31932510294810.22052/mir.2020.213088.1189ENSima Saadat-AkhtarDepartment of Mathematics,
Faculty of Basic Sciences,
Islamic Azad University,
Central Tehran Branch, Tehran, IranShervin SahebiDepartment of Mathematics,
Faculty of Basic Sciences,
Islamic Azad University,
Central Tehran Branch, Tehran, IranJournal Article20190901Let 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.https://mir.kashanu.ac.ir/article_102948_a93fee635635058ad0063521ba55abff.pdf