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P3-isomorphisms for graphs

✍ Scribed by Aldred, R. E. L.; Ellingham, M. N.; Hemminger, R. L.; Jipsen, P.

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 204 KB
Volume: 26
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199709)26:1<35::aid-jgt5>3.0.co;2-i

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✦ Synopsis

The P 3 -graph of a finite simple graph G is the graph whose vertices are the 3-vertex paths of G, with adjacency between two such paths whenever their union is a 4-vertex path or a 3-cycle. In this paper we show that connected finite simple graphs G and H with isomorphic P 3 -graphs are either isomorphic or part of three exceptional families. We also characterize all isomorphisms between P 3 -graphs in terms of the original graphs.

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