African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 254

Full Length Research Paper

A study on hypo hamiltonian graphs

Mushtaq Ahmad Shah
  • Mushtaq Ahmad Shah
  • Department of Mathematics, CMJ University, Shillong 793003, India
  • Google Scholar


  •  Accepted: 15 January 2013
  •  Published: 30 March 2013

Abstract

 

 

A graph is said to be Hamiltonian if it contains a spanning cycle. The spanning cycle is called a Hamiltonian cycle of G and G is said to be a Hamiltonian graph. A Hamiltonian path is a path that contains all the vertices in V(G) but does not return to the vertex in which it began. A graph G is said to be hypo hamiltonian if for each vV (G), the vertex sub graph G-v is Hamiltonian. This paper shall prove that every hypo hamiltonian graph G is Hamiltonian if we make the degree of removable vertex V exactly equal to n - 1, that is,   and illustrate it by some counter examples.

 

Key words: Graphs vertex, Hamiltonian cycle, degree.