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Some notes on cycle graphs

✍ Scribed by Evelyn L. Tan

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
348 KB
Volume
105
Category
Article
ISSN
0012-365X

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✦ Synopsis

Tan, E.L., Some notes on cycle graphs, Discrete Mathematics 105 (1992) 221-226. The cycle graph C(G) of a graph G is the graph whose vertices are the chordless cycles of G and two vertices in C(G) are adjacent whenever the corresponding chordless cycles have at least one edge in common. If G is acyclic, we define C(G) = 0, the empty graph. The nth iterated cycle graph C"(G) of G is defined recursively by C"(G) = C(CnmI(G)) for n Z= 2. Based on the behavior of C"(G), a graph G can be classified as either cycle-vanishing, cycle-periodic or cycle-expanding.

A graph G is said to be cycle-vanishing if there exists an integer n such that C"(G) = 0.

This paper gives a correction to a published 'characterization' of cycle-vanishing graphs.

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