Log in

Relevant bibliographies by topics / Graph spectrum / Journal articles

To see the other types of publications on this topic, follow the link: Graph spectrum.

Journal articles on the topic 'Graph spectrum'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Graph spectrum.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Alhevaz, Abdollah, Maryam Baghipur, Hilal A. Ganie, and Yilun Shang. "The Generalized Distance Spectrum of the Join of Graphs." Symmetry 12, no. 1 (2020): 169. http://dx.doi.org/10.3390/sym12010169.

Full text

Abstract:

Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D ( G ) and diagonal matrix of the vertex transmissions T r ( G ) . We determine the spectrum of the join of two graphs and of the join of a regular graph with another graph, which is the union of two different regular graphs. Moreover, thanks to the symmetry of the matrices involved, we study the generalized distance spectrum of the graphs obtained by generalization of the join graph operation through their eig

APA, Harvard, Vancouver, ISO, and other styles

2

Li, Shuchao, and Shujing Wang. "The $A_{\alpha}$- spectrum of graph product." Electronic Journal of Linear Algebra 35 (February 1, 2019): 473–81. http://dx.doi.org/10.13001/1081-3810.3857.

Full text

Abstract:

Let $A(G)$ and $D(G)$ denote the adjacency matrix and the diagonal matrix of vertex degrees of $G$, respectively. Define $$ A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G) $$ for any real $\alpha\in [0,1]$. The collection of eigenvalues of $A_{\alpha}(G)$ together with multiplicities is called the $A_{\alpha}$-\emph{spectrum} of $G$. Let $G\square H$, $G[H]$, $G\times H$ and $G\oplus H$ be the Cartesian product, lexicographic product, directed product and strong product of graphs $G$ and $H$, respectively. In this paper, a complete characterization of the $A_{\alpha}$-spectrum of $G\square H$ for arb

APA, Harvard, Vancouver, ISO, and other styles

3

Yu, Guidong, Tao Yu, Xiangwei Xia, and Huan Xu. "Spectral Sufficient Conditions on Pancyclic Graphs." Complexity 2021 (July 15, 2021): 1–8. http://dx.doi.org/10.1155/2021/3630245.

Full text

Abstract:

A pancyclic graph of order n is a graph with cycles of all possible lengths from 3 to n . In fact, it is NP-complete that deciding whether a graph is pancyclic. Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to be pancyclic in terms of the spectral radius and the signless Laplacian spectral radius of the graph.

APA, Harvard, Vancouver, ISO, and other styles

4

Cvetkovic, Dragos. "Spectral recognition of graphs." Yugoslav Journal of Operations Research 22, no. 2 (2012): 145–61. http://dx.doi.org/10.2298/yjor120925025c.

Full text

Abstract:

At some time, in the childhood of spectral graph theory, it was conjectured that non-isomorphic graphs have different spectra, i.e. that graphs are characterized by their spectra. Very quickly this conjecture was refuted and numerous examples and families of non-isomorphic graphs with the same spectrum (cospectral graphs) were found. Still some graphs are characterized by their spectra and several mathematical papers are devoted to this topic. In applications to computer sciences, spectral graph theory is considered as very strong. The benefit of using graph spectra in treating graphs is that

APA, Harvard, Vancouver, ISO, and other styles

5

RAJASEKARAN, SANGUTHEVAR, and VAMSI KUNDETI. "SPECTRUM BASED TECHNIQUES FOR GRAPH ISOMORPHISM." International Journal of Foundations of Computer Science 20, no. 03 (2009): 479–99. http://dx.doi.org/10.1142/s0129054109006693.

Full text

Abstract:

The graph isomorphism problem is to check if two given graphs are isomorphic. Graph isomorphism is a well studied problem and numerous algorithms are available for its solution. In this paper we present algorithms for graph isomorphism that employ the spectra of graphs. An open problem that has fascinated many a scientist is if there exists a polynomial time algorithm for graph isomorphism. Though we do not solve this problem in this paper, the algorithms we present take polynomial time. These algorithms have been tested on a good collection of instances. However, we have not been able to prov

APA, Harvard, Vancouver, ISO, and other styles

6

Adiga, Chandrashekar, Kinkar Das, and B. R. Rakshith. "Some Graphs Determined by their Signless Laplacian (Distance) Spectra." Electronic Journal of Linear Algebra 36, no. 36 (2020): 461–72. http://dx.doi.org/10.13001/ela.2020.4951.

Full text

Abstract:

In literature, there are some results known about spectral determination of graphs with many edges. In [M.~C\'{a}mara and W.H.~Haemers. Spectral characterizations of almost complete graphs. {\em Discrete Appl. Math.}, 176:19--23, 2014.], C\'amara and Haemers studied complete graph with some edges deleted for spectral determination. In fact, they found that if the deleted edges form a matching, a complete graph $K_m$ provided $m \le n-2$, or a complete bipartite graph, then it is determined by its adjacency spectrum. In this paper, the graph $K_{n}\backslash K_{l,m}$ $(n>l+m)$ which is obtai

APA, Harvard, Vancouver, ISO, and other styles

7

Liu, Yu, and Lihua You. "Further Results on the Nullity of Signed Graphs." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/483735.

Full text

Abstract:

The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we apply the coefficient theorem on the characteristic polynomial of a signed graph and give two formulae on the nullity of signed graphs with cut-points. As applications of the above results, we investigate the nullity of the bicyclic signed graphΓ∞p,q,l, obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.

APA, Harvard, Vancouver, ISO, and other styles

8

Iranmanesh, Mohammad, and Mahboubeh Saheli. "Toward a Laplacian spectral determination of signed ∞-graphs." Filomat 32, no. 6 (2018): 2283–94. http://dx.doi.org/10.2298/fil1806283i.

Full text

Abstract:

A signed graph consists of a (simple) graph G=(V,E) together with a function ? : E ? {+,-} called signature. Matrices can be associated to signed graphs and the question whether a signed graph is determined by the set of its eigenvalues has gathered the attention of several researchers. In this paper we study the spectral determination with respect to the Laplacian spectrum of signed ?-graphs. After computing some spectral invariants and obtain some constraints on the cospectral mates, we obtain some non isomorphic signed graphs cospectral to signed ?-graphs and we study the spectral character

APA, Harvard, Vancouver, ISO, and other styles

9

Sciriha, Irene. "Joining Forces for Reconstruction Inverse Problems." Symmetry 13, no. 9 (2021): 1687. http://dx.doi.org/10.3390/sym13091687.

Full text

Abstract:

A spectral inverse problem concerns the reconstruction of parameters of a parent graph from prescribed spectral data of subgraphs. Also referred to as the P–NP Isomorphism Problem, Reconstruction or Exact Graph Matching, the aim is to seek sets of parameters to determine a graph uniquely. Other related inverse problems, including the Polynomial Reconstruction Problem (PRP), involve the recovery of graph invariants. The PRP seeks to extract the spectrum of a graph from the deck of cards each showing the spectrum of a vertex-deleted subgraph. We show how various algebraic methods join forces to

APA, Harvard, Vancouver, ISO, and other styles

10

Urakawa, Hajime. "The Spectrum of an Infinite Graph." Canadian Journal of Mathematics 52, no. 5 (2000): 1057–84. http://dx.doi.org/10.4153/cjm-2000-044-2.

Full text

Abstract:

AbstractIn this paper, we consider the (essential) spectrum of the discrete Laplacian of an infinite graph. We introduce a new quantity for an infinite graph, in terms of which we give new lower bound estimates of the (essential) spectrum and give also upper bound estimates when the infinite graph is bipartite. We give sharp estimates of the (essential) spectrum for several examples of infinite graphs.

APA, Harvard, Vancouver, ISO, and other styles

11

SUNTORNPOCH, BORWORN, and YOTSANAN MEEMARK. "CAYLEY GRAPHS OVER A FINITE CHAIN RING AND GCD-GRAPHS." Bulletin of the Australian Mathematical Society 93, no. 3 (2016): 353–63. http://dx.doi.org/10.1017/s0004972715001380.

Full text

Abstract:

We extend spectral graph theory from the integral circulant graphs with prime power order to a Cayley graph over a finite chain ring and determine the spectrum and energy of such graphs. Moreover, we apply the results to obtain the energy of some gcd-graphs on a quotient ring of a unique factorisation domain.

APA, Harvard, Vancouver, ISO, and other styles

12

Ghorbani, M., and M. Songhori. "On the spectrum of Cayley graphs." Algebra and Discrete Mathematics 30, no. 2 (2020): 194–206. http://dx.doi.org/10.12958/adm544.

Full text

Abstract:

The set of eigenvalues of the adjacency matrix of a graph is called the spectrum of it. In the present paper, we introduce the spectrum of Cayley graphs of order pqr in terms of character table, where p,q,r are prime numbers. We also, stablish some properties of Cayley graphs of non-abelian groups with a normal symmetric connected subset.

APA, Harvard, Vancouver, ISO, and other styles

13

Alhevaz, Abdollah, Maryam Baghipur, and Somnath Paul. "Spectrum of graphs obtained by operations." Asian-European Journal of Mathematics 13, no. 02 (2018): 2050045. http://dx.doi.org/10.1142/s179355712050045x.

Full text

Abstract:

The distance signless Laplacian matrix of a simple connected graph [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the distance matrix of [Formula: see text] and [Formula: see text] is the diagonal matrix whose main diagonal entries are the vertex transmissions in [Formula: see text]. In this paper, we first determine the distance signless Laplacian spectrum of the graphs obtained by generalization of the join and lexicographic product graph operations (namely joined union) in terms of their adjacency spectrum and the eigenvalues of an auxiliary matrix, dete

APA, Harvard, Vancouver, ISO, and other styles

14

Sciriha, Irene, and Stephanie Farrugia. "On the Spectrum of Threshold Graphs." ISRN Discrete Mathematics 2011 (January 17, 2011): 1–21. http://dx.doi.org/10.5402/2011/108509.

Full text

Abstract:

The antiregular connected graph on r vertices is defined as the connected graph whose vertex degrees take the values of r−1 distinct positive integers. We explore the spectrum of its adjacency matrix and show common properties with those of connected threshold graphs, having an equitable partition with a minimal number r of parts. Structural and combinatorial properties can be deduced for related classes of graphs and in particular for the minimal configurations in the class of singular graphs.

APA, Harvard, Vancouver, ISO, and other styles

15

Palathingal, Jeepamol J., Gopalapillai Indulal, and S. Aparna Lakshmanan. "Spectrum of Gallai Graph of Some Graphs." Indian Journal of Pure and Applied Mathematics 51, no. 4 (2020): 1829–41. http://dx.doi.org/10.1007/s13226-020-0499-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Hamzeh, Asma, and Ali Ashrafi. "Spectrum and L-spectrum of the power graph and its main supergraph for certain finite groups." Filomat 31, no. 16 (2017): 5323–34. http://dx.doi.org/10.2298/fil1716323h.

Full text

Abstract:

Let G be a finite group. The power graph P(G) and its main supergraph S(G) are two simple graphs with the same vertex set G. Two elements x,y ? G are adjacent in the power graph if and only if one is a power of the other. They are joined in S(G) if and only if o(x)|o(y) or o(y)|o(x). The aim of this paper is to compute the characteristic polynomial of these graph for certain finite groups. As a consequence, the spectrum and Laplacian spectrum of these graphs for dihedral, semi-dihedral, cyclic and dicyclic groups were computed.

APA, Harvard, Vancouver, ISO, and other styles

17

Thomas, Ann Susa, Sunny Joseph Kalayathankal, and Joseph Varghese Kureethara. "An Introductory Note on the Spectrum and Energy of Molecular Graphs." Mapana - Journal of Sciences 16, no. 2 (2017): 17–27. http://dx.doi.org/10.12723/mjs.41.3.

Full text

Abstract:

Graph Theory is one branch of Mathematics that laid the foundations of the structural studies in Chemistry. The fact that every molecule or compound can be represented as a network of vertices (elements) and edges (bonds) provoked the question of the predictability of the physical and chemical properties of molecules and compounds. Spectrum, π-electron energy, Spectral Radius etc. are predictable using graph theoretical methods. This is an introductory paper about spectrum and energy of molecular graphs.

APA, Harvard, Vancouver, ISO, and other styles

18

Taheri, R., M. Behboodi, and A. Tehranian. "The spectrum subgraph of the annihilating-ideal graph of a commutative ring." Journal of Algebra and Its Applications 14, no. 08 (2015): 1550130. http://dx.doi.org/10.1142/s0219498815501303.

Full text

Abstract:

In this paper we introduce and study the spectrum graph of a commutative ring R, denoted by 𝔸𝔾s(R), that is, the graph whose vertices are all non-zero prime ideals of R with non-zero annihilator and two distinct vertices P1, P2 are adjacent if and only if P1P2 = (0). This is an induced subgraph of the annihilating-ideal graph 𝔸𝔾(R) of R. Among other results, we present the structures of all graphs which can be realized as the spectrum graph of a commutative ring. Then we show that for a non-domain Noetherian ring R, 𝔸𝔾s(R), is a connected graph if and only if 𝔸𝔾s(R) is a star graph if and only

APA, Harvard, Vancouver, ISO, and other styles

19

Nath, Rajat Kanti, and Jutirekha Dutta. "Spectrum of commuting graphs of some classes of finite groups." MATEMATIKA 33, no. 1 (2017): 87. http://dx.doi.org/10.11113/matematika.v33.n1.812.

Full text

Abstract:

In this paper, we initiate the study of spectrum of the commuting graphs of finite non-abelian groups. We first compute the spectrum of this graph for several classes of finite groups, in particular AC-groups. We show that the commuting graphs of finite non-abelian AC-groups are integral. We also show that the commuting graph of a finite non-abelian group G is integral if G is not isomorphic to the symmetric group of degree 4 and the commuting graph of G is planar. Further, it is shown that the commuting graph of G is integral if its commuting graph is toroidal.

APA, Harvard, Vancouver, ISO, and other styles

20

Zakharov, A. A., A. E. Barinov, and A. L. Zhiznyakov. "RECOGNITION OF HUMAN POSE FROM IMAGES BASED ON GRAPH SPECTRA." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-5/W6 (May 18, 2015): 9–12. http://dx.doi.org/10.5194/isprsarchives-xl-5-w6-9-2015.

Full text

Abstract:

Recognition of human pose is an actual problem in computer vision. To increase the reliability of the recognition it is proposed to use structured information in the form of graphs. The spectrum of graphs is applied for the comparison of the structures. Image skeletonization is used to construct graphs. Line segments are the nodes of the graph. The end point of line segments are the edges of the graph. The angles between adjacent segments are used to set the weights of the adjacency matrix. The Laplacian matrix is used to generate the spectrum graph. The algorithm consists of the following ste

APA, Harvard, Vancouver, ISO, and other styles

21

Coutino, Mario, Sundeep Prabhakar Chepuri, Takanori Maehara, and Geert Leus. "Fast Spectral Approximation of Structured Graphs with Applications to Graph Filtering." Algorithms 13, no. 9 (2020): 214. http://dx.doi.org/10.3390/a13090214.

Full text

Abstract:

To analyze and synthesize signals on networks or graphs, Fourier theory has been extended to irregular domains, leading to a so-called graph Fourier transform. Unfortunately, different from the traditional Fourier transform, each graph exhibits a different graph Fourier transform. Therefore to analyze the graph-frequency domain properties of a graph signal, the graph Fourier modes and graph frequencies must be computed for the graph under study. Although to find these graph frequencies and modes, a computationally expensive, or even prohibitive, eigendecomposition of the graph is required, the

APA, Harvard, Vancouver, ISO, and other styles

22

Palathingal, Jeepamol J., Aparna S. Lakshmanan, and Gopalapillai Indulal. "Spectrum of anti-gallai graph of some graphs." Indian Journal of Pure and Applied Mathematics 52, no. 1 (2021): 304–11. http://dx.doi.org/10.1007/s13226-021-00066-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Alhevaz, Abdollah, Maryam Baghipur, and Ebrahim Hashemi. "Further results on the distance signless Laplacian spectrum of graphs." Asian-European Journal of Mathematics 11, no. 05 (2018): 1850066. http://dx.doi.org/10.1142/s1793557118500663.

Full text

Abstract:

The distance signless Laplacian matrix [Formula: see text] of a connected graph [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the distance matrix of [Formula: see text] and [Formula: see text] is the diagonal matrix whose main entries are the vertex transmissions of [Formula: see text], and the spectral radius of a connected graph [Formula: see text] is the largest eigenvalue of [Formula: see text]. In this paper, first we obtain the [Formula: see text]-eigenvalues of the join of certain regular graphs. Next, we give some new bounds on the distance signles

APA, Harvard, Vancouver, ISO, and other styles

24

Cvetkovic, Dragos, and Mirko Lepovic. "Sets of cospectral graphs with least eigenvalue at least -2 and some related results." Bulletin: Classe des sciences mathematiques et natturalles 129, no. 29 (2004): 85–102. http://dx.doi.org/10.2298/bmat0429085c.

Full text

Abstract:

In this paper we study the phenomenon of cospectrality in generalized line graphs and in exceptional graphs. The paper contains a table of sets of Co spectral graphs with least eigenvalue at least ?2 and at most 8 vertices together with some comments and theoretical explanations of the phenomena suggested by the table. In particular, we prove that the multiplicity of the number 0 in the spectrum of a generalized line graph L(G) is at least the number of petals of the corresponding root graph G. .

APA, Harvard, Vancouver, ISO, and other styles

25

Atik, Fouzul, and Pratima Panigrahi. "Graphs with few distinct distance eigenvalues irrespective of the diameters." Electronic Journal of Linear Algebra 29 (September 20, 2015): 194–205. http://dx.doi.org/10.13001/1081-3810.2947.

Full text

Abstract:

The distance matrix of a simple connected graph $G$ is $D(G)=(d_{ij})$, where $d_{ij}$ is the distance between $i$th and $j$th vertices of $G$. The multiset of all eigenvalues of $D(G)$ is known as the distance spectrum of $G$. Lin et al.(On the distance spectrum of graphs. \newblock {\em Linear Algebra Appl.}, 439:1662-1669, 2013) asked for existence of graphs other than strongly regular graphs and some complete $k$-partite graphs having exactly three distinct distance eigenvalues. In this paper some classes of graphs with arbitrary diameter and satisfying this property is constructed. For ea

APA, Harvard, Vancouver, ISO, and other styles

26

Lu, Pengli, Ke Gao, and Yumo Wu. "Signless Laplacian spectrum of a class of generalized corona and its application." Discrete Mathematics, Algorithms and Applications 10, no. 05 (2018): 1850060. http://dx.doi.org/10.1142/s179383091850060x.

Full text

Abstract:

Let [Formula: see text] be a graph with [Formula: see text] edges, [Formula: see text] the subdivision graph of [Formula: see text] with [Formula: see text] the set of inserted vertices of [Formula: see text]. The generalized subdivision-edge corona graph [Formula: see text] of [Formula: see text] and [Formula: see text] is the graph obtained from [Formula: see text] and [Formula: see text] by joining the [Formula: see text]th vertex of [Formula: see text] to every vertex of [Formula: see text]. In this paper, we determine the [Formula: see text]-polynomial of the graph [Formula: see text]. Al

APA, Harvard, Vancouver, ISO, and other styles

27

Hou, Yongbo, Meifeng Dai, Changxi Dai, Tingting Ju, Yu Sun, and Weiyi Su. "Study on adjacent spectrum of two kinds of joins of graphs." Modern Physics Letters B 34, no. 16 (2020): 2050179. http://dx.doi.org/10.1142/s0217984920501791.

Full text

Abstract:

The multiple subdivision graph of a graph [Formula: see text], denoted by [Formula: see text], is the graph obtained by inserting [Formula: see text] paths of length 2 replacing every edge of [Formula: see text]. When [Formula: see text], [Formula: see text] is the subdivision graph of [Formula: see text]. Let [Formula: see text] be a graph with [Formula: see text] vertices and [Formula: see text] edges, [Formula: see text] be a graph with [Formula: see text] vertices and [Formula: see text] edges. The quasi-corona SG-vertex join [Formula: see text] of [Formula: see text] and [Formula: see tex

APA, Harvard, Vancouver, ISO, and other styles

28

Farooq, Rashid, Mehar Ali Malik, Qudsia Naureen, and Shariefuddin Pirzada. "On the nullity of a family of tripartite graphs." Acta Universitatis Sapientiae, Informatica 8, no. 1 (2016): 96–107. http://dx.doi.org/10.1515/ausi-2016-0006.

Full text

Abstract:

Abstract The eigenvalues of the adjacency matrix of a graph form the spectrum of the graph. The multiplicity of the eigenvalue zero in the spectrum of a graph is called nullity of the graph. Fan and Qian (2009) obtained the nullity set of n-vertex bipartite graphs and characterized the bipartite graphs with nullity n − 4 and the regular n-vertex bipartite graphs with nullity n − 6. In this paper, we study similar problem for a class of tripartite graphs. As observed the nullity problem in tripartite graphs does not follow as an extension to that of the nullity of bipartite graphs, this makes t

APA, Harvard, Vancouver, ISO, and other styles

29

Fiol, Miquel Àngel, Josep Fàbrega, and Victor Diego. "Equivalent Characterizations of the Spectra of Graphs and Applications to Measures of Distance-regularity." Electronic Journal of Linear Algebra 36, no. 36 (2020): 629–44. http://dx.doi.org/10.13001/ela.2020.5061.

Full text

Abstract:

The spectrum of a graph usually provides a lot of information about its combinatorial structure. Moreover, from the spectrum, the so-called predistance polynomials can be defined, as a generalization, for any graph, of the distance polynomials of a distance-regular graph. Going further, the preintersection numbers generalize the intersection numbers of a distance-regular graph. This paper describes, for any graph, the closed relationships between its spectrum, predistance polynomials, and preintersection numbers. Then, some applications to derive combinatorial properties of the given graph, mo

APA, Harvard, Vancouver, ISO, and other styles

30

Abdian, Ali Zeydi, and S. Morteza Mirafzal. "The spectral characterizations of the connected multicone graphs Kw ▽ LHS and Kw ▽ LGQ(3,9)." Discrete Mathematics, Algorithms and Applications 10, no. 02 (2018): 1850019. http://dx.doi.org/10.1142/s1793830918500192.

Full text

Abstract:

In the past decades, graphs that are determined by their spectrum have received much more and more attention, since they have been applied to several fields, such as randomized algorithms, combinatorial optimization problems and machine learning. An important part of spectral graph theory is devoted to determining whether given graphs or classes of graphs are determined by their spectra or not. So, finding and introducing any class of graphs which are determined by their spectra can be an interesting and important problem. The main aim of this study is to characterize two classes of multicone

APA, Harvard, Vancouver, ISO, and other styles

31

Paul, Somnath. "On distance and distance Laplacian spectra of corona of two graphs." Discrete Mathematics, Algorithms and Applications 08, no. 01 (2016): 1650007. http://dx.doi.org/10.1142/s1793830916500075.

Full text

Abstract:

Corona of two graphs has been defined in [F. Harary, Graph Theory (Addison-Wesley, 1969)]. In this paper, we study the distance and the distance Laplacian spectra of corona of two graphs and describe the complete distance (distance Laplacian) spectrum for some particular cases. As an application, we show that the corona operation can be used to create distance singular graphs. We also show that these results enable us to construct infinitely many pairs of distance (respectively, distance Laplacian) cospectral graphs. Last, we give a graph transformation and discuss its effect on the distance L

APA, Harvard, Vancouver, ISO, and other styles

32

Abdy, Muhammad, Rahmat Syam, and Agnes Monica Putri. "Spectrum Matriks Detour dari Graf Roda dengan n +1 Titik W_n." Journal of Mathematics, Computations, and Statistics 3, no. 1 (2020): 32. http://dx.doi.org/10.35580/jmathcos.v3i1.19901.

Full text

Abstract:

Penelitian ini bertujuan untuk menentukan spectrum matriks detour dari graf roda dengan n+1 titik Wn. Spectrum dalam teori graf merupakan suatu topik menarik untuk dikaji dengan mempertemukan teori graf dan aljabar linear. Bentuk spectrum matriks detour adalah salah satu spectrum yang dapat ditentukan dalam graf roda. Matriks berordo (2 × n) yang terdiri dari nilai eigen berbeda dan banyak basis ruang eigen dari matriks terhubung langsung graf roda merupakan spectrum dari graf roda. Hasil penelitian ini menunjukkan bahwa langkah-langkah dalam menentukan spectrum matriks detour dari graf roda n

APA, Harvard, Vancouver, ISO, and other styles

33

Rakhimberdina, Zarina, Xin Liu, and Tsuyoshi Murata. "Population Graph-Based Multi-Model Ensemble Method for Diagnosing Autism Spectrum Disorder." Sensors 20, no. 21 (2020): 6001. http://dx.doi.org/10.3390/s20216001.

Full text

Abstract:

With the advancement of brain imaging techniques and a variety of machine learning methods, significant progress has been made in brain disorder diagnosis, in particular Autism Spectrum Disorder. The development of machine learning models that can differentiate between healthy subjects and patients is of great importance. Recently, graph neural networks have found increasing application in domains where the population’s structure is modeled as a graph. The application of graphs for analyzing brain imaging datasets helps to discover clusters of individuals with a specific diagnosis. However, th

APA, Harvard, Vancouver, ISO, and other styles

34

Ganie, Hilal A. "On distance Laplacian spectrum (energy) of graphs." Discrete Mathematics, Algorithms and Applications 12, no. 05 (2020): 2050061. http://dx.doi.org/10.1142/s1793830920500615.

Full text

Abstract:

For a simple connected graph [Formula: see text] of order [Formula: see text] having distance Laplacian eigenvalues [Formula: see text], the distance Laplacian energy [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the Wiener index of [Formula: see text]. We obtain the distance Laplacian spectrum of the joined union of graphs [Formula: see text] in terms of their distance Laplacian spectrum and the spectrum of an auxiliary matrix. As application, we obtain the distance Laplacian spectrum of the lexicographic product of graphs. We study the distance Laplacian

APA, Harvard, Vancouver, ISO, and other styles

35

Balti, Marwa. "Non self-adjoint Laplacians on a directed graph." Filomat 31, no. 18 (2017): 5671–83. http://dx.doi.org/10.2298/fil1718671b.

Full text

Abstract:

We consider a non self-adjoint Laplacian on a directed graph with non symmetric edge weights. We analyse spectral properties of this Laplacian under a Kirchhoff assumption. Moreover we establish isoperimetric inequalities in terms of the numerical range to show the absence of the essential spectrum of the Laplacian on heavy end directed graphs.

APA, Harvard, Vancouver, ISO, and other styles

36

Habibi, Nader, and Ali Reza Ashrafi. "On revised szeged spectrum of a graph." Tamkang Journal of Mathematics 45, no. 4 (2014): 375–87. http://dx.doi.org/10.5556/j.tkjm.45.2014.1463.

Full text

Abstract:

The revised Szeged index is a molecular structure descriptor equal to the sum of products $[n_u(e) + \frac{n_0(e)}{2}][n_v(e) + \frac{n_0(e)}{2}]$ over all edges $e = uv$ of the molecular graph $G$, where $n_0(e)$ is the number of vertices equidistant from $u$ and $v$, $n_u(e)$ is the number of vertices closer to $u$ than $v$ and $n_v(e)$ is defined analogously. The adjacency matrix of a graph weighted in this way is called its revised Szeged matrix and the set of its eigenvalues is the revised Szeged spectrum of $G$. In this paper some new results on the revised Szeged spectrum of graphs are

APA, Harvard, Vancouver, ISO, and other styles

37

Jog, S. R., and Raju Kotambari. "On the Adjacency, Laplacian, and Signless Laplacian Spectrum of Coalescence of Complete Graphs." Journal of Mathematics 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/5906801.

Full text

Abstract:

Coalescence as one of the operations on a pair of graphs is significant due to its simple form of chromatic polynomial. The adjacency matrix, Laplacian matrix, and signless Laplacian matrix are common matrices usually considered for discussion under spectral graph theory. In this paper, we compute adjacency, Laplacian, and signless Laplacian energy (Qenergy) of coalescence of pair of complete graphs. Also, as an application, we obtain the adjacency energy of subdivision graph and line graph of coalescence from itsQenergy.

APA, Harvard, Vancouver, ISO, and other styles

38

Imran, Muhammad, Yasir Ali, Mehar Ali Malik, and Kiran Hasnat. "Chromatic spectrum of some classes of 2-regular bipartite colored graphs." Journal of Intelligent & Fuzzy Systems 41, no. 1 (2021): 1125–33. http://dx.doi.org/10.3233/jifs-210066.

Full text

Abstract:

Chromatic spectrum of a colored graph G is a multiset of eigenvalues of colored adjacency matrix of G. The nullity of a disconnected graph is equal to sum of nullities of its components but we show that this result does not hold for colored graphs. In this paper, we investigate the chromatic spectrum of three different classes of 2-regular bipartite colored graphs. In these classes of graphs, it is proved that the nullity of G is not sum of nullities of components of G. We also highlight some important properties and conjectures to extend this problem to general graphs.

APA, Harvard, Vancouver, ISO, and other styles

39

Balinska, Krystyna, Dragos Cvetkovic, Zoran Radosavljevic, Slobodan Simic, and Dragan Stevanovic. "A survey on integral graphs." Publikacije Elektrotehnickog fakulteta - serija: matematika, no. 13 (2002): 42–65. http://dx.doi.org/10.2298/petf0213042b.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Jordan, Jonathan. "SPECTRUM OF THE LAPLACIAN OF AN ASYMMETRIC FRACTAL GRAPH." Proceedings of the Edinburgh Mathematical Society 49, no. 1 (2006): 101–13. http://dx.doi.org/10.1017/s001309150400063x.

Full text

Abstract:

AbstractWe consider a simple self-similar sequence of graphs that does not satisfy the symmetry conditions that imply the existence of a spectral decimation property for the eigenvalues of the graph Laplacians. We show that, for this particular sequence, a very similar property to spectral decimation exists, and we obtain a complete description of the spectra of the graphs in the sequence.

APA, Harvard, Vancouver, ISO, and other styles

41

Breen, Jane, Steve Butler, Nicklas Day, et al. "Computing Kemeny's constant for a barbell graph." Electronic Journal of Linear Algebra 35 (December 9, 2019): 583–98. http://dx.doi.org/10.13001/ela.2019.5175.

Full text

Abstract:

In a graph theory setting, Kemeny’s constant is a graph parameter which measures a weighted average of the mean first passage times in a random walk on the vertices of the graph. In one sense, Kemeny’s constant is a measure of how well the graph is ‘connected’. An explicit computation for this parameter is given for graphs of order n consisting of two large cliques joined by an arbitrary number of parallel paths of equal length, as well as for two cliques joined by two paths of different length. In each case, Kemeny’s constant is shown to be O(n3), which is the largest possible order of Kemeny

APA, Harvard, Vancouver, ISO, and other styles

42

Huang, Shaobin, Jiang Zhou, and Changjiang Bu. "Signless Laplacian spectral characterization of graphs with isolated vertices." Filomat 30, no. 14 (2016): 3689–96. http://dx.doi.org/10.2298/fil1614689h.

Full text

Abstract:

A graph is said to be DQS if there is no other non-isomorphic graph with the same signless Laplacian spectrum. For a DQS graph G, we show that G ? rK1 is DQS under certain conditions. Applying these results, some DQS graphs with isolated vertices are obtained.

APA, Harvard, Vancouver, ISO, and other styles

43

Díaz, Roberto, and Oscar Rojo. "Effects on the distance Laplacian spectrum of graphs with clusters by adding edges." Electronic Journal of Linear Algebra 35 (November 26, 2019): 511–23. http://dx.doi.org/10.13001/ela.2019.5163.

Full text

Abstract:

All graphs considered are simple and undirected. A cluster in a graph is a pair of vertex subsets (C, S), where C is a maximal set of cardinality |C| ≥ 2 of independent vertices sharing the same set S of |S| neighbors. Let G be a connected graph on n vertices with a cluster (C, S) and H be a graph of order |C|. Let G(H) be the connected graph obtained from G and H when the edges of H are added to the edges of G by identifying the vertices of H with the vertices in C. It is proved that G and G(H) have in common n −|C| + 1 distance Laplacian eigenvalues, and the matrix having these common eigenv

APA, Harvard, Vancouver, ISO, and other styles

44

Tsiovkina, L. "The prime spectrum of an automorphism group of an 𝐴𝑇4(𝑝,𝑝+2,𝑟)-graph". St. Petersburg Mathematical Journal 32, № 5 (2021): 917–28. http://dx.doi.org/10.1090/spmj/1677.

Full text

Abstract:

The present paper is devoted classification of A T 4 ( p , p + 2 , r ) \mathrm {AT4}(p,p+2,r) -graphs. There is a unique A T 4 ( p , p + 2 , r ) \mathrm {AT4}(p,p+2,r) -graph with p = 2 p=2 , namely, the distance-transitive Soicher graph with intersection array { 56 , 45 , 16 , 1 ; 1 , 8 , 45 , 56 } \{56, 45, 16, 1;1, 8, 45, 56\} , whose local graphs are isomorphic to the Gewirtz graph. The existence of an A T 4 ( p , p + 2 , r ) \mathrm {AT4}(p,p+2,r) -graph with p > 2 {p>2} remains an open question. It is known that the local graphs of each A T 4 ( p , p + 2 , r ) \mathrm {AT4}(p,p+2,r

APA, Harvard, Vancouver, ISO, and other styles

45

Cardoso, Domingos, Paula Carvalho, Paula Rama, Slobodan Simic, and Zoran Stanic. "Lexicographic polynomials of graphs and their spectra." Applicable Analysis and Discrete Mathematics 11, no. 2 (2017): 258–72. http://dx.doi.org/10.2298/aadm1702258c.

Full text

Abstract:

For a (simple) graph H and non-negative integers c0, c1,..., cd (cd ? 0), p(H) = ?dk=0 ck?Hk is the lexicographic polynomial in H of degree d, where the sum of two graphs is their join and ck?Hk is the join of ck copies of Hk. The graph Hk is the kth power of H with respect to the lexicographic product (H0 = K1). The spectrum (if H is connected and regular) and the Laplacian spectrum (in general case) of p(H) are determined in terms of the spectrum of H and ck's. Constructions of infinite families of cospectral or integral graphs are announced.

APA, Harvard, Vancouver, ISO, and other styles

46

Abdollahi, Alireza, Shahrooz Janbaz, and Mojtaba Jazaeri. "Groups all of whose undirected Cayley graphs are determined by their spectra." Journal of Algebra and Its Applications 15, no. 09 (2016): 1650175. http://dx.doi.org/10.1142/s0219498816501759.

Full text

Abstract:

The adjacency spectrum [Formula: see text] of a graph [Formula: see text] is the multiset of eigenvalues of its adjacency matrix. Two graphs with the same spectrum are called cospectral. A graph [Formula: see text] is “determined by its spectrum” (DS for short) if every graph cospectral to it is in fact isomorphic to it. A group is DS if all of its Cayley graphs are DS. A group [Formula: see text] is Cay-DS if every two cospectral Cayley graphs of [Formula: see text] are isomorphic. In this paper, we study finite DS groups and finite Cay-DS groups. In particular we prove that a finite DS group

APA, Harvard, Vancouver, ISO, and other styles

47

Andjelic, Milica, Tamara Koledin, and Zoran Stanic. "Distance spectrum and energy of graphs with small diameter." Applicable Analysis and Discrete Mathematics 11, no. 1 (2017): 108–22. http://dx.doi.org/10.2298/aadm1701108a.

Full text

Abstract:

In this paper we express the distance spectrum of graphs with small diameter in terms of the eigenvalues of their adjacency matrix. We also compute the distance energy of particular types of graph and determine a sequence of infinite families of distance equienergetic graphs.

APA, Harvard, Vancouver, ISO, and other styles

48

Sharafdini, R., and A. Z. Abdian. "Signless Laplacian determinations of some graphs with independent edges." Carpathian Mathematical Publications 10, no. 1 (2018): 185–96. http://dx.doi.org/10.15330/cmp.10.1.185-196.

Full text

Abstract:

Let $G$ be a simple undirected graph. Then the signless Laplacian matrix of $G$ is defined as $D_G + A_G$ in which $D_G$ and $A_G$ denote the degree matrix and the adjacency matrix of $G$, respectively. The graph $G$ is said to be determined by its signless Laplacian spectrum (DQS, for short), if any graph having the same signless Laplacian spectrum as $G$ is isomorphic to $G$. We show that $G\sqcup rK_2$ is determined by its signless Laplacian spectra under certain conditions, where $r$ and $K_2$ denote a natural number and the complete graph on two vertices, respectively. Applying these resu

APA, Harvard, Vancouver, ISO, and other styles

49

Gopalapillai, Indulal. "Distance spectrum of graph compositions." Ars Mathematica Contemporanea 2, no. 1 (2009): 93–100. http://dx.doi.org/10.26493/1855-3974.103.e09.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Orden, David, Ivan Marsa-Maestre, Jose Manuel Gimenez-Guzman, and Enrique de la Hoz. "Bounds on spectrum graph coloring." Electronic Notes in Discrete Mathematics 54 (October 2016): 63–68. http://dx.doi.org/10.1016/j.endm.2016.09.012.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!