Introduction

Abstract

Let Γ-(V, E) be a simple undirected graph without loops. The adjacency relation in Γ will usually be denoted as ~. A clique of Γ is a set of mutually adjacent vertices. A clique is called maximal if it is not properly contained in another clique. We will denote the distance between two vertices x and y of Γ by d(x, y). If X₁ and X₂ are two nonempty sets of vertices, then we denote by d(X₁, X₂) the minimal distance between a vertex of X₁ and a vertex of X₂. If X₁ is a singleton {x₁}, then we will also write d(x₁, X₂) instead of d({x₁}, X₂). For every i∈ ℕ and every nonempty set X of vertices, we denote by Γ_i(X) the set of all vertices y for which d(y, X)=i. If X is a singleton {x}, then we also write Γ_i(x) instead of Γ_i({x}).