论文信息 - On the Structure of Hamiltonian Cycles in Cayley Graphs of Finite Quotients of the Modular Group

On the Structure of Hamiltonian Cycles in Cayley Graphs of Finite Quotients of the Modular Group

It is a fairly longstanding conjecture that if G is any finite group with ¦G¦s > 2 and if X is any set of generators of G then the Cayley graph Γ(G : X) should have a Hamiltonian cycle. We present experimental results found by computer calculation that support the conjecture. It turns out that in the case where G is a finite quotient of the modular group the Hamiltonian cycles possess remarkable structural properties.

Paul E. Schupp

[1] Kevin Keating,et al. On Hamilton Cycles in Cayley Ghaphs in Groups with Cyclic Commutator Subgroup , 1985 .

[2] N. J. A. Sloane,et al. Gray codes for reflection groups , 1989, Graphs Comb..

[3] Dave Witte. Cayley digraphs of prime-power order are Hamiltonian , 1986 .

[4] Jonathan L. Alperin,et al. Groups and Representations , 1995 .

[5] G. A. Miller. On the groups generated by two operators , 1901 .

[6] A. M. Macbeath,et al. Generators of the linear fractional groups , 1969 .

[7] Aner Shalev,et al. Classical groups, probabilistic methods, and the (2,3)-generation problem , 1996 .

[8] Jeffrey D. Ullman,et al. Introduction to Automata Theory, Languages and Computation , 1979 .

[9] Henry H. Glover,et al. A Hamilton cycle in the Cayley graph of the <2, p, 3> presentation of PSL2(p) , 1996, Discret. Math..

[10] D. West. Introduction to Graph Theory , 1995 .

[11] W. Magnus,et al. Combinatorial Group Theory: COMBINATORIAL GROUP THEORY , 1967 .

[12] R. Rankin. A campanological problem in group theory. II , 1966, Mathematical Proceedings of the Cambridge Philosophical Society.

[13] Joseph A. Gallian,et al. Hamiltonian cycles and paths in Cayley graphs and digraphs - A survey , 1996, Discret. Math..