For an even graph G and non-negative integers r and s, the pair \((r,\,s)\) is an admissible pair if \(4r+8s=|E(G)|.\) If G admits a decomposition into r copies of \(C_4,\) the cycle of length four, and s copies of \(C_8,\) the cycle of length eight, for every admissible pair \((r,\,s),\) then G has a \(\{C_4^r,\,C_8^s\}\)-decomposition. In this paper, a necessary and sufficient condition is obtained for the existence of a \(\{C_4^r,\,C_8^s\}\)-decomposition of the complete k-partite graph \(K_{a_1,\,a_2,\,\dots ,\,a_k},\) where \(k\ge 3.\) Further, a characterization is obtained for the graph \(K_m\times K_n,\) where \(\times\) denotes the tensor product of graphs, to admit a \(\{C_4^r,\,C_8^s\}\)-decomposition.

对于偶数图表ģ和非负整数ř和小号，一对\（（R，\，S）\）是受理对如果\（4R + 787-8 = | E（G）|。\）如果ģ坦言对于每个允许对\（（r，\，s），\），将分解为长度为4的循环\（C_4，\）的r个副本和分解为长度为8的循环的\（C_8，\）的s副本。那么G有一个\（\ {C_4 ^ r，\，C_8 ^ s \} \）-分解。本文为\（\ {C_4 ^ r，\，C_8 ^ s \} \）的存在获得了充要条件。完整的-decomposition ķ -partite图表\（{K_ A_1，\，A_2，\，\点，\，a_k}，\）其中\（K \ GE 3. \）此外，对于图中所获得的特征\（K_m \ times K_n，\）其中\（\ times \）表示图的张量积，以接受\（\ {C_4 ^ r，\，C_8 ^ s \} \）分解。