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Let $n \geq 4$ be an even integer and $W_n$ be the wheel graph with $n$vertices. The distance $d_{ij}$ between any two distinct vertices $i$ and $j$of $W_n$ is the length of the shortest path connecting $i$ and $j$. Let $D$ bethe $n \times n$ symmetric matrix with diagonal entries equal to zero andoff-diagonal entries equal to $d_{ij}$. In this paper, we find a positivesemidefinite matrix $\widetilde{L}$ such that ${\rm rank}(\widetilde{L})=n-1$,all row sums of $\widetilde{L}$ equal to zero and a rank one matrix $ww^T$ suchthat \[D^{-1}=-\frac{1}{2}\widetilde{L} + \frac{4}{n-1}ww^T. \] An interlacingproperty between the eigenvalues of $D$ and $\widetilde{L}$ is also proved.

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