Periphery with respect to cliques in graphs

Abstract

In this paper we introduce the concepts of vertex-to-clique periphery, clique-to-vertex periphery and clique-to-clique periphery in a connected graph. We investigate their properties and determine them for certain classes of graphs. We also find the relations of these with the periphery, center, vertex-to-clique center, clique-to-vertex center and clique-to-clique center of certain classes of graphs.

Keywords and phrases:

• Clique
• galaxy
• center
• periphery
• (ζ, S)-center
• (V, ζ)-center
• (ζ, V)-center
• (ζ, ζ)-center
• (V, ζ)-periphery
• (ζ, V)-periphery
• (ζ, ζ)-periphery