Document Type

Article

Publication Date

2010

Source Publication

Australasian Journal of Combinatorics

Abstract

A domination graph of a digraph D, dom(D), is created using the vertex set of D, V(D). There is an edge uv in dom(D) whenever (u, z) or (v, z) is in the arc set of D, A(D), for every other vertex z ε V(D). For only some digraphs D has the structure of dom(D) been characterized. Examples of this are tournaments and regular digraphs. The authors have characterizations for the structure of digraphs D for which UG(D) = dom(D) or UG(D) ≅ dom(D). For example, when UG(D) ≅ dom(D), the only components of the complement of UG(D) are complete graphs, paths and cycles. Here, we determine values of i and j for which UG(D) ≅ dom(D) and UGC(D) = C4 υ Pi υ Pj.

Comments

Published version. Australasian Journal of Combinatorics, Volume 48 (2010), Publication’s website. Used with permission.