Journal of Graph Theory
Characterizing bipartite Toeplitz graphs
Theoretical Computer Science
On Hamiltonian Toeplitz graphs
Discrete Mathematics
On the chromatic number of Toeplitz graphs
Discrete Applied Mathematics
| Hi-index | 0.04 |
Let n,a"1,...,a"k be distinct positive integers. A finite Toeplitz graph T"n(a"1,...,a"k)=(V,E) is a graph where V={v"0,...,v"n"-"1} and E={(v"i,v"j):|i-j|@?{a"1,...,a"k}}. In this paper, we characterize bipartite finite Toeplitz graphs with k@?3. In most cases, the characterization takes O(loga"3) arithmetic steps; in the remaining cases, it takes O(a"1). A consequence of the proposed results is the complete characterization of the chromatic number of finite Toeplitz graphs with k@?3. In addition, we characterize some classes of infinite bipartite Toeplitz graphs with k=4.