Characterization of special hamiltonian graphs

Abstract

We get a formula for the number of hamiltonian circuits of a graph through which we characterize the special hamiltonian graphs, that is containing a dominant circuit of minimal length. (2000): 05C45. Mathematics Subject Classification

Some necessary conditions for a graph to be hamiltonian

“…Evidently c j i is the number of the edges through V with Hamiltonian index b i . By Theorem 1. it follows(2). By (i = 0, ∀j = 2, .…”

“…We say that C is Hamiltonian if it contains all the vertices of G. The graph G is said to be Hamiltonian if it contains a Hamiltonian circuit. In [2] we denote by N H the number of the Hamiltonian circuits of G, and call Hamiltonian index of an edge of G the number b of the Hamiltonian circuits of G through . In [2] we prove the following theorem: By this theorem we get some necessary conditions for the Hamiltonianity of a graph.…”