An inverse formula for the distance matrix of a wheel graph with an even number of vertices

Let n ? 4 be an even integer and W the wheel graph with vertices. The distance d i j between any two distinct vertices of is length shortest path connecting . D × symmetric matrix diagonal entries equal to zero off-diagonal In this paper, we find a positive semidefinite L ˜ such that rank ( ) = ? 1 , all row sums zero, one w T 2 + An interlacing property eigenvalues also proved.