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Random Walks On Regular Polyhedra And Other Distance–Regular Graphs

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  • A.R.D. van Slijpe

Abstract

In this paper we consider Markov chains of the following type: the state space is the set of vertices of a connected, regular graph, and for each vertex transitions are to the adjacent vertices, with equal probabilities. When the mean first–passage matrix F of such a Markov chain is symmetric, the expectation and variance of first–entrance times, recurrence times, number of visits to a vertex and the expectation of the number of different vertices visited, can easily be computed from the entries of F. The method is most effective, when the underlying graph is distance–regular; then F is symmetric and the entries of F can easily be obtained from the graph.

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  • A.R.D. van Slijpe, 1984. "Random Walks On Regular Polyhedra And Other Distance–Regular Graphs," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 38(4), pages 273-292, December.
    • Handle: RePEc:bla:stanee:v:38:y:1984:i:4:p:273-292
    DOI: 10.1111/j.1467-9574.1984.tb01118.x
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