On the Symmetry of Cubic Graphs

Abstract

Let G be a connected finite graph in which each edge has two distinct ends and no two distinct edges have the same pair of ends. We suppose further that G is cubic , that is, each vertex is incident with just three edges. An s-path in G, where s is any positive integer, is a sequence S = (v 0 , v 1 … , v s ) of s + 1 vertices of G, not necessarily all distinct, which satisfies the following two conditions: (i) Any three consecutive terms of S are distinct. (ii) Any two consecutive terms of S are the two ends of some edge of G.