Nonisomorphic Maximum Packing and Minimum Covering of K v with 8-Cycles

The maximum packing C ₈-max PD(v) and minimum covering C ₈-minCD(v) of K _v with 8-cycles are studied, all structures with the nonisomorphic leave (excess) are presented. In Li et al. (Graphs Combin 25:735–752, 2009), C ₈-max PD(v) and C ₈-minCD(v) have been determined for odd v. In this paper, we introduce the enumeration of nonisomorphic ${(v,\frac{v}{2}+s)}$ -graphs (s = 4, 6), give complete solution of the maximum packing and minimum covering designs of K _v with 8-cycles for any even v with all possible leaves (excesses).