4 - Spectrum and Automorphism Group
from Part III - Properties of the Shrikhande Graph
Published online by Cambridge University Press: 05 June 2026
Summary
We saw earlier that the Shrikhande graph is a strongly regular graph, with parameters (16,6,2,2). In Chapter 3, we saw that this implies that the adjacency matrix A satisfies the two equations
AJ = 6J, A2 = 4I + 2J,
where I and J are the identity and all-1 matrices of order 16.
The first equation shows that the all-1 vector j is an eigenvector of A with eigenvalue 6. From the theory of real symmetric matrices we know that any other eigenvector v is orthogonal to j, and hence if the corresponding eigenvalue is θ.
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- The Shrikhande GraphA Window on Discrete Mathematics, pp. 59 - 65Publisher: Cambridge University PressPrint publication year: 2026
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