Ralph P. Grimaldi

Integer-Distance Graphs

Abstract This paper presents an extended discussion on a family of graphs and their complements. The discussion includes the derivations of several numeric parameters of the graphs, such as the sizes of their edge sets, their independence numbers, and their clique numbers. Furthermore, it is shown that these complements are unit interval graphs - hence chordal, and perfect, while the original family comprises graphs that are comparability graphs of semiorders and these are perfect though not generally chordal.