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On a Result of Aleliunas et al. Concerning Random Walks on Graphs

Published online by Cambridge University Press:  27 July 2009

José Luis Palacios
José Luis Palacios
Affiliation:
Department of Mathematics New JerseyInstitute of Technology Newark, New Jersey 07102
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Abstract

Aleliunas et al. [3] proved that for a random walk on a connected raph G = (V, E) on N vertices, the expected minimum number of steps to visit all vertices is bounded by 2|E|(N - 1), regardless of the initial state. We give here a simple proof of that result through an equality involving hitting times of vertices that can be extended to an inequality for hitting times of edges, thus obtaining a bound for the expected minimum number of steps to visit all edges exactly once in each direction.

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Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 4 , Issue 4 , October 1990 , pp. 489 - 492
Copyright
Copyright © Cambridge University Press 1990

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References

REFERENCES

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