PlanarGraph

PlanarGraph[{e1,e2,…}] yields a planar graph with edges ej.

PlanarGraph[{v1,v2,…},{e1,e2,…}] yields a planar graph with vertices vi and edges ej.

PlanarGraph[{…,wi[vi],…},{…,wj[ej],…}] yields a planar graph with vertex and edge properties defined by the symbolic wrappers wk.

PlanarGraph[{vi->vj,…}] uses rules vi->vj to specify a planar graph.

Please visit the official Wolfram Language Reference for more details and examples on core symbols.