A graph is edge-transitive if its automorphism group acts transitively on its edges.In this paper,we give a characterization of connected edge-transitive trivalent graphs of order ℓp,where p is a prime andℓ(0＜ℓ＜p)is an integer.Applying this characterization,we first give a classification of connected semi-symmetric trivalent graphs of order ℓp with 0＜ℓ≤54 and p a prime,and then we show that all connected edge-transitive trivalent graphs of order ℓp with 0＜ℓ≤100 and p a prime are known.
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