Pancyclicity and Cayley Graphs on Abelian Groups

Abstract

Abstract:We prove that connected Cayley graphs of valency at least 3 on abelian groups are even edge-pancyclic and have cycles of every possible odd length bigger than or equal to the odd girth. C 2012 Wiley Periodicals, Inc. J. Graph

Pancyclicity and Cayley graphs on generalized dihedral groups

“…We can then use a 3-bypass vertically on each edge of the matching edges until we reach a cycle C * using all the vertices of the first i columns except u i ,1 . So C * has length 2i − 1 and we are done when i = m. 2 . We now have a vertical edge on the right from which we can construct 3-bypasses to the right to reach a cycle of length 2m − 1.…”

“…The cited papers all studied subclasses of either circulant graphs or n-dimensional cubes. The following theorem [2] then considerably generalized that work by completely describing what happens for Cayley graphs on abelian groups. Theorem 1.1.…”