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UPPER AND LOWER BOUNDS FOR THE POWER OF EIGENVALUES IN SEIDEL MATRIX
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 Title & Authors
UPPER AND LOWER BOUNDS FOR THE POWER OF EIGENVALUES IN SEIDEL MATRIX
IRANMANESH, ALI; FARSANGI, JALAL ASKARI;
 
 Abstract
In this paper, we generalize the concept of the energy of Seidel matrix S(G) which denoted by Sα(G) and obtain some results related to this matrix. Also, we obtain an upper and lower bound for Sα(G) related to all of graphs with |detS(G)| ≥ (n - 1); n ≥ 3.
 Keywords
Graph eigenvalue;Seidel matrix;Conference matrix;Power of eigenvalue;Nonlinear programming;KKT method;
 Language
English
 Cited by
1.
Seidel-Estrada index, Journal of Inequalities and Applications, 2016, 2016, 1  crossref(new windwow)
 References
1.
J. Abadie, On the Kuhn-Tucker Theorem in Nonlinear Programming, 19-36, North Holland, Amsterdam, 1967.

2.
M.S. Bazaraa, H.D. Sherali and C.M. Shetty, Nonlinear Programming Theory and Algo-rithms, John Wiley & Sons, NewYork, NY,second ed, 1993.

3.
V. Belevitch, Conference networks and Hadamard matrices, Ann. Soc. Sci. Bruxelles 82, Ser. I. (1968), 13-32.

4.
G. Bennett, p-free lp-inequalities, Amer. Math. Monthly. 117 (2010), 334-351. crossref(new window)

5.
J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, Macmillan, 1976.

6.
A.E. Brouwer and W.H. Haemers, Spectra of Graphs, Springer, New York, 2012.

7.
E.Ghorbani, On eigenvalues of Seidel matrices and Haemers'conjecture, http://arxiv.org/abs/1301.0075v1, (2013).

8.
H. Finner, Some new inequalities for the range distribution, with application to the deter-mination of optimum significance levels of multiple range tests, J. Amer. Statist. Assoc. 85 (1990), 191-194. crossref(new window)

9.
I. Gutman, The energy of a graph: Old and new results, in: A. Betten, A. Kohner, R. Laue, A. Wassermann (Eds.), Algebraic Combinatorics and Applications, Springer, Berlin, 2001, 196-211.

10.
W.H. Haemers, Seidel switching and graph energy, MATCH Commun. Math. Comput. Chem. 68 (2012), 653-659.

11.
O.L. Mangasarian and S. Fromovitz, The Fritz John necessary optimality conditions in the presence of equality and inequality constraints, J. Math. Anal. Appl. 17 (1967), 37-47. crossref(new window)

12.
J. Nocedal and S.J. Wright, Numerical Optimization, Second Edition, Springer, New York, 2006.

13.
J.H. Van Lint and J.J. Seidel, Equilateral point sets in elliptic geometry, Indag. Math. 28 (1966), 335-348. crossref(new window)