Research Manuscripts from Student Work in MAT289.23 (now MAT268):

A. Aguado, S.I. El-Zanati, H. Hake, J. Stob, and H. Yayla, On rho-labeling the union of three cycles, Australasian Journal of Combinatorics, to appear. [Spring 2004]

In the above manuscript it is shown that if G is the union of three cycles, then G admits a rho-labeling. The manuscript contains 5 new theorems. Each of the student authors proved at least one theorem.

A. Aguado and S.I. El-Zanati, On sigma-labeling the union of three cycles, Journal of Combinatorial Mathematics and Combinatorial Computing, to appear. [Spring 2004]

In the above manuscript it is shown that if G with n edges is the union of three cycles, then G admits a sigma-labeling if and only if n = 0 or 3 (mod 4).

R.C. Bunge, S.I. El-Zanati, and C. Vanden Eynden, on gamma-labelings of almost-bipartite graphs, in preparation. [Spring 2005]

In the above manuscript it is shown that if G_1 has a modified gamma-labeling and if G_2, G_3, …, G_t have alpha-labelings, then G_1 U G_2 U G_3 U … U G_t has a gamma-labeling. It is also shown that if  G is a 2-regular almost-bipartite graph and G is not in {C_3, C_3 U C_4}, then G has a gamma-labeling.

S.I. El-Zanati and B.M. Frank, On gamma-labeling the intersection of cycles, in preparation. [Spring 2005]

In the above manuscript it is shown that if G consits of r C_{4x+1} that share a single edge (and are vertex-disjoint otherwise), then G admits a gamma-labeling.