Nonisomorphic Maximum Packing and Minimum Covering of K_v with 8-Cycles

摘要

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,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).