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Eigenvalue properties of adjacency matrix of a graph.
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An adjacency matrix of a graph contains degrees of vertices as the diagonal elements and 0 or -1 as other values. We know one of its eigenvalues has to be 0 as determinant of the matrix is 0. Also, sum of eigenvalues will be sum of diagonal elements which is number of edges of the graph. I want to know some other property related to the eigenvalues of such a matrix.
Specifically, I want to know if 1 can be among the remaining eigenvalues (except 0) and how will it affect other values.
Thanks for help 😊
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