Some Families of Fixed Points for the Eccentric Digraph Operator

Marr, Alison

Denman, Richard

Anthony, Barbara M.

2019-09-18

2019-09-18

2011-08

Anthony, Barbara & Denman, Richard & Marr, Alison. (2011). Some families of fixed points for the eccentric digraph operator. JCMCC. The Journal of Combinatorial Mathematics and Combinatorial Computing. 78.

http://collections.southwestern.edu/s/suscholar/item/248

We investigate the existence of fixed point families for the eccentric digraph (ED) operator, which was introduced in [1]. In [2], the notion of the period ρ(G) of a digraph G (under the ED operator) was defined, and it was observed, but not proved, that for any odd positive integer m, Cm × Cm is periodic, and that ρ(ED(Cm × Cm)) = 2ρ(ED(Cm)). Also in [2], the following question was posed: which digraphs are fixed points under the digraph operator? We provide a proof for the observations about Cm ×Cm, and in the process show that these products comprise a family of fixed points under ED. We then provide a number of other interesting examples of fixed point families.

English

The Charles Babbage Research Centre

Fixed point families

Eccentric digraph operator

en_US Article