On the Symmetry of Cubic Graphs

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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 = (v0, v1… , vs) 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.

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