Electronic Resource
Springer
Annals of combinatorics
3 (1999), S. 475-481
ISSN:
0219-3094
Keywords:
60J15
;
82B41
;
random walks
;
graphs
;
adjacency matrix
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The problem of a restricted random walk on graphs, which keeps track of the number of immediate reversal steps, is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the number ofn-step walks withr reversal steps for walks on any graph. In the case of graphs of a uniform valence, we show that our result has a probabilistic meaning, and deduce explicit expressions for the generating function in terms of the eigenvalues of the adjacency matrix. Applications to periodic lattices and the complete graph are given.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01608798
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