Graph-theoretic properties Dürer graph

the dürer graph graph formed vertices , edges of dürer solid. cubic graph of girth 3 , diameter 4. construction skeleton of dürer s solid, can obtained applying y-Δ transform opposite vertices of cube graph, or generalized petersen graph g(6,2). graph of convex polyhedron, dürer graph 3-vertex-connected simple planar graph.

the dürer graph well-covered graph, meaning of maximal independent sets have same number of vertices, four. 1 of 4 well-covered cubic polyhedral graphs , 1 of 7 well-covered 3-connected cubic graphs. other 3 well-covered simple convex polyhedra tetrahedron, triangular prism, , pentagonal prism.

the dürer graph hamiltonian, lcf notation [-4,5,2,-4,-2,5;-]. more precisely, has 6 hamiltonian cycles, each pair of may mapped each other symmetry of graph.