The sequence y = 122112122122.. . given by W. Kolakoski in [ 1] can be described as a sequence of lâ€™s and 2â€™s having the property that the length of the jth run of like symbols is equal to the jthâ€¦ (More)

The queenâ€™s graph Qn has the squares of the n Ã— n chessboard as its vertices; two squares are adjacent if they are in the same row, column, or diagonal. Let Î³(Qn) and i(Qn) be the minimum sizes of aâ€¦ (More)

For a permutation Ï€ of the vertex set of a graph G, the graph Ï€G is obtained from two disjoint copies G1 and G2 of G by joining each v in G1 to Ï€(v) in G2. Hence if Ï€ = 1, then Ï€G = K2 Ã— G, the prismâ€¦ (More)

Denote the n Ã— n toroidal queens graph by Qn. We show that Î³(Q3k) = k + 2 when k â‰¡ 0, 3, 4, 6, 8, 9 (mod 12). This completes the proof that Î³(Q3k) = 2k âˆ’ Î²(Qk) for all positive integers k.

Let Î³ (n) be the number of C-words of length n. Say that a C-word w is left doubly extendable (LDE) if both 1w and 2w are C. We show that for any positive real number Ï† and positive integer N suchâ€¦ (More)

Denote the n Ã— n toroidal queenâ€™s graph by Qn. We find its automorphism group Aut(Qn) for each positive integer n, showing that for n â‰¥ 6, Aut(Qn) is generated by the translations, the group of theâ€¦ (More)