Determination of Hamiltonian Circuit and Euler Trail from a Given Graphic Degree Sequence

Abstract

A sequence of nonnegative integers can represent degrees of a graph. Already there is an established condition under which the above conclusion is true. It is our objective in this paper to show that a similar degree sequence represents degrees of vertices of a graph having Hamiltonian Circuit or Euler Tour. The only fallacy of the conclusion is that there may be graphs those are not Hamiltonian or Euler graphs may have the same degree sequence.