The Relationship Between Difference Digraphs And Doubly Regular Asymmetric Digraphs

The definition of difference digraphs is put forward firstly by Luis Marinez in2009.It is a kind of digraph, In this kind of figure, the determine of the direction is relatedto the difference of module has two equivalent definition chose is based on the questionsstudied.In1987, Noboru Ito fist proposed the concept of doubly regular asymmetric digraphsand have studied the interrelated figure and simple nature. The doubly regular asym-metric digraphs is a very important kind of directed graphs. In2003, Yury J. Ionina andHadi Kharaghani have constructed five doubly regular asymmetric digraphs with differentparaments. The definition of digraphs shows that any digraphs can be seen as a specialdifference digraphs.This paper mainly studied the relationship between the difference digraphs and dou-bly regular asymmetric digraphs.In the paper, according to the definition and nature of the doubly regular asymmetricdigraphs, firstly proposed the sufficient and necessary condition between the differencedigraphs and doubly regular asymmetric digraphs.Secondly, according to the sufficient and necessary condition between the differencedigraphs and doubly regular asymmetric digraphs, using the difference set construct thefirst and the second class of doubly regular asymmetric digraphs.