Abstract
A formula for computing the resistance between any two vertices in the stellated graph of a regular graph is obtained. It turns out that the two-point resistance of the stellated graph can be expressed in terms of the two-point resistance of the original graph. As a consequence, the Kirchhoff index (i.e. the sum of the effective resistances between all pairs of vertices) for the stellated graph is obtained, which extends the previously known result. The correspondence between random walks and electric networks is then used to obtain the mean first passage time and mean commute time for random walks on stellated graphs.
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