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Pancyclicity of connected circulant graphs
Author(s) -
Bogdanowicz Z. R.
Publication year - 1996
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199606)22:2<167::aid-jgt7>3.0.co;2-l
Subject(s) - circulant matrix , combinatorics , mathematics , circulant graph , vertex (graph theory) , discrete mathematics , graph , line graph , graph power
The circulant G n ( a 1 , ⋖, a k ), where 0 < a 1 < ··· < a k < ( n + 1)/2, is defined as the vertex‐transitive graph that has vertices i ± a 1 , ···, i ± 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. © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 17–25, 1997