Abstract
This paper examines the Hamiltonicity of graphs having some hidden behaviours of some other graphs in it. The well-known mathematician Barnette introduced the open conjecture which becomes a theorem by restricting our attention to the class of graphs which is 3-regular, 3- connected, bipartite, planar graphs having odd number of vertices in its partition be proved as a Hamiltonian. Consequently the result proved in this paper stated that “Every connected vertex-transitive simple graph has a Hamilton path” shows a significant improvement over the previous efforts by L.Babai and L.Lovasz who put forth this conjecture. And we characterize a graphic sequence which is forcibly Hamiltonian if every simple graph with degree sequence is Hamiltonian. Thus we discussed about the concealed graphs which are proven to be Hamiltonian.
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