Regularity in Semigraphs

In this article, we have introduced a variety of regular semigraphs using the concept of the degree of a vertex in a semigraph. The concept of the degree of a vertex has variations due to the variety of vertices (end vertex, mid vertex, and mid-end vertex) in semigraphs. Two more regular semigraphs have been defined with the help of the binomial incidence matrix of a semigraph which determines the semigraph uniquely up to isomorphism. The interconnection between the variety of regular semigraphs has been discussed. In the latter part, the minimum number of edges in the semigraph which is regular of all kinds have been given.