• CONDITION FOR HAMILTONIANCITY

Abstract

AHamiltonian path is a spanning path in a graph i.e. a path through every vertex. The problem of determining if a graph is Hamiltonian is well known to be NP-complete while there are several necessary condition for a hamiltonianicity, the search continue for sufficient conditions in this paper  I shall prove that every simple graph of order (2n+1)  and degree of each vertex is   2n respectively n N then G  is Hamiltonian. In fact it has n edge-disjoint Hamiltonian circuits.