Abstract
Let be the fan graph with vertices. The distance between any two distinct vertices i and j of is the length of the shortest path connecting i and j. Let be the symmetric matrix with diagonal entries equal to zero and off-diagonal entries equal to . In this paper, we find two positive semidefinite matrices and such that , all row sums of and are equal to zero, and find two rank one matrices and such that The interlacing property between the eigenvalues of and (resp., ) is also established.
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