Degree Sequence of Tight Distance Graphs

A graph G on n vertices is a tight distance graph if there exists a set D⊆{1,2,…,n−1} such that V(G)={0,1,…,n−1} and ij∈E(G) if and only if |i−j|∈D. A characterization of the degree sequences of tight distance graphs is given. This characterization yields a fast method for recognizing and realizing degree sequences of tight distance graphs.