Cyclic Decomposition of $k$-Permutations and Eigenvalues of the Arrangement Graphs

[摘要] The $(n,k)$-arrangement graph $A(n,k)$ is a graph with all the $k$-permutations of an $n$-element set as vertices where two $k$-permutations are adjacent if they agree in exactly $k-1$ positions. We introduce a cyclic decomposition for $k$-permutations an

[学科分类] 离散数学和组合数学

[关键词] $k$-permutation;cyclic decomposition;arrangement graph;eigenvalue of graph