Abstract：In order to study acyclic edge coloring of Meredith graphs and series-parallel graphs, matrix analysis, mathematical induction as well as color-changing technique were employed in the study. The results show that for Meredith graphs, the equation a' (G) = Δ (G_k) is proved. Meanwhile, for series-parallel graphs of Δ (G_k) ≥5, a' (G) ≤ Δ (G) + 1 is also proved.

Keyword：series-parallel graphs;Meredith graphs;matrix analysis;acyclic edge coloring;