Star edge-coloring of a class of cactus graphs

In the report， a star edge-coloring of a graph $G$ is a proper edge coloring without 2-colored paths or cycles of length 4. The star chromatic index of $G$，${{\chi }^{\mathrm{\text{'}}}}_{st}(G)$，indicates that $G$ has a star edge-coloring with the smallest number. The cactus graph is a connected graph of which each block is a cycle or an edge. The mathematical induction is performed to obtain a class of cactus graphs $C_n\cdot C_m(n\ge \mathrm{3},m\ge \mathrm{3})$， and which are generalized.