On powers of circular arc graphs and proper circular arc graphs

摘要

In this paper it is shown that the class X of circular arc graphs is closed under the operation of power; this means, G ∈X implies G∈X for any positive integer k Furthermore, implies and if diam(G~k) 4 then G~k∈X implies . Another result on the powers of directed graphs is that if Gk belongs to the class of in-, out-, or local tournaments, then so does Gk+1. This result is used to prove the closedness of proper circular arc graphs under the power operation.