2020-07-14T14:31:21Z
http://mir.kashanu.ac.ir/?_action=export&rf=summon&issue=12945
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
Mathematical Chemistry Works of Dragos Cvetkovic
Ivan
Gutman
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
chemical graph theory
molecular graph
Huckel molecular orbital theory
2019
12
01
129
136
http://mir.kashanu.ac.ir/article_95507_bbf21ebf318b0d63b6a7ed64364739ab.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
Seidel Integral Complete Split Graphs
Pavel
Hic
Milan
Pokorny
Dragan
Stevanovic
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
2019
12
01
137
150
http://mir.kashanu.ac.ir/article_96006_a1c746b4ddcdc566dcd6fa5e65f3851b.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
Oboudi-Type Bounds for Graph Energy
Ivan
Gutman
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
2019
12
01
151
155
http://mir.kashanu.ac.ir/article_96938_7a344e0905c77f7e7c5531dd406edc2c.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
A Study of PageRank in Undirected Graphs
Abdollah
Lotfi
Modjtaba
Ghorbani
Hamid
Mesgarani
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
2019
12
01
157
169
http://mir.kashanu.ac.ir/article_100994_4a176ba385e4ccacb68137f1ffe36250.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
Note on the Sum of Powers of Normalized Signless Laplacian Eigenvalues of Graphs
Ş. Burcu
Bozkurt Altındağ
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.
Normalized signless Laplacian eigenvalues
Randic (normalized) incidence energy
Bound
2019
12
01
171
182
http://mir.kashanu.ac.ir/article_101587_6d3f9f9d05078067f97d041c27644362.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
The Fourth and Fifth Laplacian Coefficients of some Rooted Trees
Mahsa
Arabzadeh
Gholam-Hossein
Fath-Tabar
Hamid
Rasoli
Abolfazl
Tehranian
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).
Graph
Eigenvalue
Laplacian matrix
Laplacian coefficient
2019
12
01
183
192
http://mir.kashanu.ac.ir/article_101588_f54ef31c99328589cc826b00c2bd8846.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
A Multiplicative Version of Forgotten Topological Index
Asghar
Yousefi
Ali
Iranmanesh
Andrey
Dobrynin
Abolfazl
Tehranian
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
2019
12
01
193
211
http://mir.kashanu.ac.ir/article_102000_e2b2c1124183c3b89ccf0bc81f103cf6.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
On the Configurations with n Points and Two Distances
Ali Asghar
Rezaei
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
2019
12
01
213
225
http://mir.kashanu.ac.ir/article_45816_fa687f17a0883ef1c1290ad251cdd442.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
Trees with Extreme Values of Second Zagreb Index and Coindex
Reza
Rasi
Seyed Mahmoud
Sheikholeslami
Afshin
Behmaram
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
2019
12
01
227
238
http://mir.kashanu.ac.ir/article_64769_94f1d4167b1f10a85ce4b7a462e66070.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
Distinguishing Number and Distinguishing Index of the Join of Two Graphs
Saeid
Alikhani
Samaneh
Soltani
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.
Distinguishing index
distinguishing number
join
2019
12
01
239
251
http://mir.kashanu.ac.ir/article_102109_ff92223a27f0fd1dfbcd2f75fc2bc091.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
Probabilistic Properties of F-indices of Trees
Hadis
Morovati
Ramin
Kazemi
Akram
Kohansal
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
2019
12
01
253
261
http://mir.kashanu.ac.ir/article_102110_03ce4c5cdfca7c2b30cafd5a8b6251ba.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
Classification of Bounded Travelling Wave Solutions of the General Burgers-Boussinesq Equation
Rasool
Kazemi
Masoud
Mossadeghi
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
2019
12
01
263
279
http://mir.kashanu.ac.ir/article_33673_c46440a9ce390b0837c9ce8d88d78e80.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
Graph Invariants of Deleted Lexicographic Product of Graphs
Bahare
Akhavan Mahdavi
Mostafa
Tavakoli
Freydoon
Rahbarnia
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
2019
12
01
281
291
http://mir.kashanu.ac.ir/article_102486_8728c06bbd29a7f7c9f2daefaaa2fa55.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
Best Proximity Point Theorems for Ciric Type G-Contractions in Metric Spaces with a Graph
Kamal
Fallahi
Mohammad
Hamidi
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
2019
12
01
293
304
http://mir.kashanu.ac.ir/article_102487_bffa611422018a74ee8545663dd0461f.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
k-Intersection Graph of a Finite Set
Fahimeh
Esmaeeli
Ahmad
Erfanian
Farzaneh
Mansoori
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
2019
12
01
305
317
http://mir.kashanu.ac.ir/article_102613_b205b739f72772023b0d554c0ed5cdc2.pdf
Mathematics Interdisciplinary Research
Math. Interdisc. Res.
2538-3639
2538-3639
2019
4
2
On Eigenvalues of Permutation Graphs
Sima
Saadat-Akhtar
Shervin
Sahebi
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
2019
12
01
319
325
http://mir.kashanu.ac.ir/article_102948_a93fee635635058ad0063521ba55abff.pdf