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Pancyclicity of connected circulant graphs

✍ Scribed by Bogdanowicz, Z. R.

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 299 KB
Volume: 22
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199606)22:2<167::aid-jgt7>3.0.co;2-l

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✦ Synopsis

The circulant G,(al,. . . , ak), where 0 < al < ... < a k < ( n + 1 ) / 2 , is defined as the vertex-transitive graph that has vertices ifal,. . . ,if a k (mod n) adjacent to each vertex i. In this work we show that the connected circulants of degree at least three contain all even cycles. In addition, we prove that the connected circulants of girth three contain cycles of all lengths. 0 1996 John Wiley &Sons, Inc.

EDGE-BIPANCYCLIC CIRCULANTS

To present our main result for even cycles (Theorem 1) we need the following two lemmas.

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