Abstract
Petersen graph plays a significant role in graph theory, it gives a clear picture of some problems in graph theory. Petersen graph has many properties that make it fascinating. In this paper, the idea about the concytic points is introduced in order to prove that Petersen graph is non-Hamiltonian graph. We give a kind of elementary proof that Petersen graph is non-planar graph. At the same time, Petersen graph, as a non-bipartite graph, has been proved as the direct corollary of Ko?nig theorem. At the end of the article, hierarchical label was introduced and the isomorphic was proved between various representations of Petersen graph.
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