Which platonic graphs are hamiltonian

Frucht, A canonical representation of trivalent Hamiltonian graphs, J. Graph Theor. Garey, D. Freeman, Gordon, Y. Orlovich, F. Werner, Hamiltonian properties of triangular grid graphs, Discrete Math. Harary, Graph theory , Addison-Wesley, Hung, F. Keshavarz-Kohjerdi, C. Lin, J. Chen, The Hamiltonian connectivity of alphabet supergrid graphs, Int. Imran, H. Siddiqui, Computing the metric dimension of convex polytopes generated by wheel related graphs, Acta Math.

Kewen, H. Lai, J. Zhou, Hamiltonian-connected graphs, Comput. Xiong, Every 4—connected line graph is Hamiltonian if and only if it is Hamiltonian connected, In: R. Kuzel, Hamiltonian properties of graphs , Ph. D Thesis, U. Pilsen, Lukovits, Indicators for atoms included in cycles, J. Lukovits, The detour index, Croat.

Acta , 69 , — Lukovits, M. Razinger, On calculation of the detour index, J. Ore, Hamilton-connected graphs, J. Pure Appl. Qiang, Z. Qain, A. Yahui, The Hamiltonicity of generalized honeycomb torus networks, Inf. Raza, S. Hayat, X. Pan, Binary locating-dominating sets in rotationally-symmetric convex polytopes, Symmetry , 10 , — Pan, On the fault-tolerant metric dimension of convex polytopes, Appl.

Raza, J. Liu, S. Shabbir, M. Nadeem, T. Zamfirescu, The property of Hamiltonian connectedness in Toeplitz graphs, Complexity , , Stewart, Sufficient conditions for Hamiltonicity in multiswapped networks, J. Parallel Distrib. Thomassen, Hamiltonian-connected tournaments, J. Theory B , 28 , — Quantum Chem. Wei, Hamiltonian paths and Hamiltonian connectivity in graphs, Discrete Math.

Wei, Z. You, H. Yang, J. Du, L. Summary [ edit ] Description Hamiltonian platonic graphs. Only the octahedron has an Eulerian path, made by extending the Hamiltonian path with the dotted path.

Source Own work Author Cmglee. I, the copyright holder of this work, hereby publish it under the following licenses:. You may select the license of your choice. You cannot overwrite this file. The following other wikis use this file: Usage on en.

Short title Hamiltonian platonic graphs Image title Orthographic projections and planar graphs of Hamiltonian cycles of the vertices of the five Platonic solids by CMG Lee. Structured data Items portrayed in this file depicts. Wikimedia username : Cmglee. Creative Commons Attribution-ShareAlike 4.

Categories : trimetric projection All Platonic solids Platonic graphs Hamiltonian paths Eulerian paths. Namespaces File Discussion.

Views View Edit History.