RESULTS ON THE EULER-SEIDEL MATRIX

2016 ◽  
Vol 38 (5) ◽  
pp. 431-456
Author(s):  
Nesrin Tutaş
Keyword(s):  
Seidel Matrix

scholarly journals On the Seidel Energy of Certain Mesh Derived Networks

2019 ◽  
Vol 9 (2) ◽  
pp. 1905-1910
Keyword(s):  
Adjacency Matrix ◽  
Seidel Matrix ◽  
Energy Of Graph ◽  
The Absolute ◽  
Manual Calculation

The energy of graph G is defined as the sum of the absolute values of eigenvalues of the adjacency matrix A(G). The manual calculation of energy of graphs consumes several man hours. In this paper, we use MATLAB to generate the Seidel matrix and hence calculate the Seidel energy of some mesh derived networks.

scholarly journals QLS-integrality of complete r-partite graphs

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1043-1051 ◽  
Author(s):  
Milan Pokorný
Keyword(s):  
Sufficient Conditions ◽  
Open Problems ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Signless Laplacian ◽  
Seidel Matrix ◽  
Complete Multipartite

A graph G is called A-integral (L-integral, Q-integral, S-integral) if the spectrum of its adjacency (Laplacian, signless Laplacian, Seidel) matrix consists entirely of integers. In this paper we study connections between the Q-(L,S,A) integral complete multipartite graphs. Moreover, new sufficient conditions for a construction of infinite families of QLS-integral complete r''-partite graphs Kp1,p2,...,pr'' = Kb1?p1,b2?p2,...,bs?ps from given QLS-integral r'-partite graphs Kp1,p2,...,pr' = Ka1?p1,a2?p2,...,as?ps are given. Using these conditions new infinite classes of such graphs for s = 4, 5, 6 are constructed, which affirmatively answers to questions proposed by Wang, Zhao and Li in [10, 14]. Finally, we propose open problems for further study.

scholarly journals UPPER AND LOWER BOUNDS FOR THE POWER OF EIGENVALUES IN SEIDEL MATRIX

2015 ◽  
Vol 33 (5_6) ◽  
pp. 627-633 ◽  
Author(s):  
ALI IRANMANESH ◽  
JALAL ASKARI FARSANGI
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Seidel Matrix

Some properties of eigenvalues of the Seidel matrix

2020 ◽  
pp. 1-12
Author(s):  
Saieed Akbari ◽  
Jalal Askari ◽  
Kinkar Chandra Das
Keyword(s):  
Seidel Matrix

Four‐component surface‐consistent deconvolution

Geophysics ◽  
1993 ◽  
Vol 58 (3) ◽  
pp. 383-392 ◽  
Author(s):  
Peter W. Cary ◽  
Gary A. Lorentz
Keyword(s):  
Seismic Data ◽  
Random Noise ◽  
Three Dimensional ◽  
Convincing Evidence ◽  
Structural Effects ◽  
Common Depth Point ◽  
Amplitude Spectra ◽  
Data Volume ◽  
Ground Roll ◽  
Seidel Matrix

When performing four‐component surface‐consistent deconvolution, it is assumed that the decomposition of amplitude spectra into source, receiver, offset, and common‐depth‐point components enables accurate deconvolution filters to be derived. However, relatively little effort has been put into the verification of this assumption. Some verification of the assumption is available by analyzing the results of the surface‐consistent decomposition of real seismic data. The surface‐consistent log‐amplitude spectra of land seismic data are able to provide convincing evidence that the source component collects effects of the source signature and near‐source structural effects, and that the receiver component collects receiver characteristics and near‐receiver structural effects. In addition, the offset component collects effects due to ground roll and average reflectivity, and the CDP component collects mostly random noise unless it is constrained to be smooth. Based on the results of this analysis, deconvolution filters should be constructed from the source and receiver components, while the offset and CDP components are discarded. The four‐component surface‐consistent decomposition can be performed efficiently by making use of a simple rearrangement of the Gauss‐Seidel matrix inversion equations. The algorithm requires just two passes through the prestack data volume, regardless of the sorted order of the data, so it is useful for both two‐dimensional and three‐dimensional (2-D and 3-D) data volumes.

scholarly journals Seidel energy of complete multipartite graphs

2021 ◽  
Vol 9 (1) ◽  
pp. 212-216
Author(s):  
Mohammad Reza Oboudi
Keyword(s):  
Simple Graph ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Seidel Matrix ◽  
The Absolute ◽  
Complete Multipartite

Abstract The Seidel energy of a simple graph G is the sum of the absolute values of the eigenvalues of the Seidel matrix of G. In this paper we study the Seidel eigenvalues of complete multipartite graphs and find the exact value of the Seidel energy of the complete multipartite graphs.

scholarly journals Seidel Equienergetic Graphs

2016 ◽  
Vol 16 ◽  
pp. 62-69
Author(s):  
Harishchandra S. Ramane ◽  
Mahadevappa M. Gundloor ◽  
Sunilkumar M. Hosamani
Keyword(s):  
Characteristic Polynomial ◽  
Regular Graphs ◽  
Seidel Matrix ◽  
The Absolute ◽  
Equienergetic Graphs ◽  
Square Matrix

The Seidel matrix S(G) of a graph G is the square matrix with diagonal entries zeroes and off diagonal entries are – 1 or 1 corresponding to the adjacency and non-adjacency. The Seidel energy SE(G) of G is defined as the sum of the absolute values of the eigenvalues of S(G). Two graphs G1 and G2 are said to be Seidel equienergetic if SE(G1) = SE(G2). We establish an expression for the characteristic polynomial of the Seidel matrix and for the Seidel energy of the join of regular graphs. Thereby construct Seidel non cospectral, Seidel equienergetic graphs on n vertices, for all n ≥ 12

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