The line digraph of a regular and pancircular digraph is also regular and pancircular

Abstract

This paper introduces thepancircularity property on digraphs: a digraphD is said to bepancircular if it contains circuits of every lengthL for all 1 ≦L ≦ # E(D). We discuss preservation of pancircularity under the line-digraph operation, and prove the theorem stated in the title. As a corollary, all DeBruijn graphs are proved to be pancyclic and pancircular.