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Adjacency matrix, Order and Valency

Let A be the adjacency matrix of a regular graph of order v and valency k. Let J be the all-ones matrix of the same order. Show that

A*J = J*A = K*J

"Definition 2.1 A graph r with adjacency matrix A = A(r) is called regular if
there exists a natural number k such that AJ = JA = kJ. The number k is called valency of r."

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