Abstract
A symmetric, random walk on a graph G can be defined by prescribing weights to the edges in such a way that for each vertex the sum of the weights of the edges incident to the vertex is at most one. The fastest mixing, Markov chain (FMMC) problem for G is to determine the weighting that yields the fastest mixing random walk. We solve the FMMC problem in the case that G is the union of two complete graphs.
Acknowledgements
The authors thank the referee for thoughtful comments and suggestions that improved this article exposition.
Notes
1. This remark also follows from extending the definition of u and v to allow real values and noting that ρ2 is continuous on Mark(G).