# Combinatorial Mathematics X: Proceedings of the Conference by C. C. Chen, N. Quimpo (auth.), Louis Reynolds Antoine Casse

By C. C. Chen, N. Quimpo (auth.), Louis Reynolds Antoine Casse (eds.)

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Extra info for Combinatorial Mathematics X: Proceedings of the Conference held in Adelaide, Australia, August 23–27, 1982

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A finite dihedral group is R-sequenceable if and only if its order is a multiple of 4, see [17]. The question as to which dihedral groups are sequenceable seems to be more difficult. The groups D 3 and D 4 of orders 6 and 8 respectively are not sequenceable. The groups Dn, 3 < n < 37, [10]. n odd, are sequenceable The groups Dp,p prime and p ~ I mod 4 are sequenceable [5]. Also, the groups Dp, p prime, p ~ 7 mod 8 and for which 2 belongs to the exponent ½(p-l) are sequenceable [10]. D 6 and D 8 are sequenceable.

3. increasing Now g ( 3 ) = 5 and It is possible, though that g(7) ) g(9). c(m, n) ~ C(p, q). If we consider C(m, I) + C(m + i, 0), then the smallest value of m for 45 which this implication is known to fail is m = 9. (a) Does C(m, I) ÷ C(m + I, 0) for 2 ~ m ( 8? The Petersen graph shows that C(9, I) ÷ C(lO, O) and this is because P is hypohamiltonlan. In other words, P is not hamiltonian but every vertex deleted subgraph of P is. (b) Does C(m - i) ÷ C(m + I, O) hypohamiltoniangraph if and only if there exists a of order m?

Koblitz, p-adic Numbers, p-adic Analysis, and Zeta Functions. (Springer, 1977). [i0] B. Mazur, Eigenvalues fields, ~ o c . S~pos. of Frobenius acting on algebraic varieties over finite Pure Math. 29 (1975), 231-261. M. Schmidt, Equations over Finite Fields, an Elementary Approach. Notes in Mathematics 536, Springer, (Lecture 1976). J. Schoof, Unpublished manuscript. T. Tate, The arithmetic of elliptic curves, Invent. Math. 23 (1974), 179-206. [14] E. Ughi, On the number of points of elliptic curves over a finite field and a problem of B.