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 i j ∈ 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.