✦ LIBER ✦

Unusual random walks

✍ Scribed by Milan Randic; Wayne L. Woodworth; Ante Graovac

Publisher: John Wiley and Sons
Year: 1983
Tongue: English
Weight: 794 KB
Volume: 24
Category: Article
ISSN: 0020-7608
DOI: 10.1002/qua.560240503

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

For most structures (molecules, graphs, lattices) a count of random walks for nonequivalent sites will give different numbers, particularly for walks of many steps. Occasionally one finds the same count of walks for nonequivalent sites. These have been termed “unusual walks” and have been closely examined in the case of trivalent graphs. While it remains to be understood what structural factors are critical, some regularities have been observed and are discussed. Unusual walks within a single structure signal “isospectural” points in a graph. A number of structures possessing unusual walks have been displayed, and a few constructive steps which do not alter the “unusual” characteristics of selected vertices have been indicated.

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