Highly irregular graphs

  title={Highly irregular graphs},
  author={Yousef Alavi and Gary Chartrand and Fan Chung Graham and Paul Erd{\"o}s and Ronald L. Graham and Ortrud R. Oellermann},
  journal={Journal of Graph Theory},
A connected graph is highly irregular if each of its vertices is adjacent only to vertices with distinct degrees. In this paper we investigate several problems concerning the existence and enumeration of highly irregular graphs as well as their independence numbers, with particular focus on the corresponding problems for highly irregular trees.