Geodesic
Main eigenvalues of real symmetric matrices with application to signed graphs
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1091-1102 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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An eigenvalue of a real symmetric matrix is called main if there is an associated eigenvector not orthogonal to the all-1 vector ${\bf j}$. Main eigenvalues are frequently considered in the framework of simple undirected graphs. In this study we generalize some results and then apply them to signed graphs.
An eigenvalue of a real symmetric matrix is called main if there is an associated eigenvector not orthogonal to the all-1 vector ${\bf j}$. Main eigenvalues are frequently considered in the framework of simple undirected graphs. In this study we generalize some results and then apply them to signed graphs.
DOI : 10.21136/CMJ.2020.0147-19
Classification : 05C22, 05C50
Keywords: main angle; signed graph; adjacency matrix; Laplacian matrix; Gram matrix 
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Stanić, Zoran. Main eigenvalues of real symmetric matrices with application to signed graphs. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1091-1102. doi: 10.21136/CMJ.2020.0147-19

[1] Cardoso, D. M., Sciriha, I., Zerafa, C.: Main eigenvalues and $(\kappa, \tau)$-regular sets. Linear Algebra Appl. 432 (2010), 2399-2408. | DOI | MR | JFM

[2] Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs: Theory and Applications. J. A. Barth Verlag, Heidelberg (1995). | MR | JFM

[3] Cvetković, D., Rowlinson, P., Simić, S.: An Introduction to the Theory of Graph Spectra. London Mathematical Society Student Texts 75, Cambridge University Press, Cambridge (2010). | DOI | MR | JFM

[4] Deng, H., Huang, H.: On the main signless Laplacian eigenvalues of a graph. Electron. J. Linear Algebra 26 (2013), 381-393. | DOI | MR | JFM

[5] Doob, M.: A geometric interpretation of the least eigenvalue of a line graph. Combinatorial Mathematics and its Applications R. C. Bose, T. A. Dowling University of North Carolina, Chapel Hill (1970), 126-135. | MR | JFM

[6] Haynsworth, E. V.: Applications of a theorem on partitioned matrices. J. Res. Natl. Bur. Stand., Sec. B 63 (1959), 73-78. | DOI | MR | JFM

[7] Hou, Y., Tang, Z., Shiu, W. C.: Some results on graphs with exactly two main eigenvalues. Appl. Math. Lett. 25 (2012), 1274-1278. | DOI | MR | JFM

[8] Hou, Y., Zhou, H.: Trees with exactly two main eigenvalues. J. Nat. Sci. Hunan Norm. Univ. 28 (2005), 1-3 Chinese. | MR | JFM

[9] Petersdorf, M., Sachs, H.: Über Spektrum, Automorphismengruppe und Teiler eines Graphen. Wiss. Z. Tech. Hochsch. Ilmenau 15 (1969), 123-128 German. | MR | JFM

[10] Rowlinson, P.: The main eigenvalues of a graph: A survey. Appl. Anal. Discrete Math. 1 (2007), 445-471. | DOI | MR | JFM

[11] Stanić, Z.: Inequalities for Graph Eigenvalues. London Mathematical Society Lecture Note Series 423, Cambridge University Press, Cambridge (2015). | DOI | MR | JFM

[12] Stanić, Z.: Bounding the largest eigenvalue of signed graphs. Linear Algebra Appl. 573 (2019), 80-89. | DOI | MR | JFM

[13] Zaslavsky, T.: Matrices in the theory of signed simple graphs. Advances in Discrete Mathematics and Applications B. D. Acharya, G. O. H. Katona, J. Nešetřil Ramanujan Mathematical Society Lecture Notes Series 13, Ramanujan Mathematical Society, Mysore (2010), 207-229. | MR | JFM

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