The Main Eigenvalues of a Graph : a Survey

@inproceedings{Rowlinson2007TheME,
  title={The Main Eigenvalues of a Graph : a Survey},
  author={Peter Rowlinson},
  year={2007}
}
Let G be a simple graph with vertex set V (G) = {1, 2, . . . , n} and (0, 1)adjacency matrix A. The eigenvalue μ of A is said to be a main eigenvalue of G if the eigenspace E(μ) is not orthogonal to the all-1 vector j. An eigenvector x is a main eigenvector if xj 6= 0. The main eigenvalues of the connected graphs of order ≤ 5 are listed in [12, Appendix B], and those of all the connected graphs on 6 vertices are given in [10]. In this section we introduce notation and survey the basic results… CONTINUE READING
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