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- W1569256616 abstract "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 and show that this gives rise to a very fine equitable partition of A(n,k). This equitable partition can be employed to compute the complete set of eigenvalues (of the adjacency matrix) of A(n,k). Consequently, we determine the eigenvalues of A(n,k) for small values of k. Finally, we show that any eigenvalue of the Johnson graph J(n,k) is an eigenvalue of A(n,k) and that -k is the smallest eigenvalue of A(n,k) with multiplicity O(n^k) for fixed k." @default.
- W1569256616 created "2016-06-24" @default.
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- W1569256616 date "2013-08-26" @default.
- W1569256616 modified "2023-09-27" @default.
- W1569256616 title "Cyclic decomposition of k-permutations and eigenvalues of the arrangement graphs" @default.
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