Determining the Component Number of Links Corresponding to Triangular and Honeycomb Lattices

Abstract

There is a classical correspondence between edge-signed plane graphs and link diagrams. Determining component number of links corresponding to plane graphs may be one of the first problems in studying links by using graphs. There has been several early studies in this aspect, for example, the component number of links formed from 2-dimensional square lattices (44) has been determined. In this paper, we determine the component number of links corresponding to 2-dimensional triangular (36) and honeycomb (63) lattices with free or cyclic boundary condition.