A graph is called k-regular if k edges meet at each vertex. Let G be a k-regular
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A graph is called k-regular if k edges meet at each vertex. Let G be a k-regular graph.
(a) Show that the adjacency matrix A of G has λ = k as an eigenvalue.
(b) Show that if A is primitive, then the other eigenvalues are all less than k in absolute value.
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a Each column of A sums to k since each vertex connects to k others Thus A kP ...View the full answer
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