A survey of antiregular graphs

Abstract

The set of all different degrees of the vertices of a graph G is known as the degree set of G. A nontrivial graph of order n whose degree set consists of n−1 elements is called an antiregular graph. Antiregular graphs have been studied in literature also under other names, including "quasi-perfect graphs", "maximally nonregular graphs" and "degree antiregular graphs". This paper aims to gather the known results concerning the antiregular graphs.