Some Families of Fixed Points for the Eccentric Digraph Operator

Title

Some Families of Fixed Points for the Eccentric Digraph Operator

Creator

Marr, Alison

Denman, Richard

Anthony, Barbara M.

Date

2019-09-18

Date Available

2019-09-18

Date Issued

2011-08

Identifier

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.

uri

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

Abstract

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.

Language

English

Publisher

The Charles Babbage Research Centre

Subject

Fixed point families

Eccentric digraph operator

Type

en_US Article