Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Degree with Neighborhood Conditions and Highly Hamiltonian Graphs

Degree with Neighborhood Conditions and Highly Hamiltonian Graphs In 1997 Bollobás and Thomason (J. Graph Theory 26:165–173, 1997) and Brandt (Discrete Appl. Math. 79:63–66, 1997) defined the weakly pancyclic. In this paper we define weakly vertex-pancyclic and obtain a new sufficient condition for graph to be weakly vertex-pancyclic as the following: if G is a 2-connected graph of order n, and $\{|N(u)\cup N(v)|+d(w):u,v,w\in V(G),uv\not\in E(G)$ , wu, or $wv\not\in E(G)\}\geq n+1$ , then G is weakly vertex-pancyclic. This result also implies a conjecture of Faudree et al. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Degree with Neighborhood Conditions and Highly Hamiltonian Graphs

Acta Applicandae Mathematicae , Volume 109 (2) – Oct 5, 2008

Loading next page...
 
/lp/springer-journals/degree-with-neighborhood-conditions-and-highly-hamiltonian-graphs-wOsyX0Gdnj

References (12)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science+Business Media B.V.
Subject
Mathematics; Mechanics; Statistical Physics, Dynamical Systems and Complexity; Theoretical, Mathematical and Computational Physics; Computer Science, general; Mathematics, general
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-008-9328-x
Publisher site
See Article on Publisher Site

Abstract

In 1997 Bollobás and Thomason (J. Graph Theory 26:165–173, 1997) and Brandt (Discrete Appl. Math. 79:63–66, 1997) defined the weakly pancyclic. In this paper we define weakly vertex-pancyclic and obtain a new sufficient condition for graph to be weakly vertex-pancyclic as the following: if G is a 2-connected graph of order n, and $\{|N(u)\cup N(v)|+d(w):u,v,w\in V(G),uv\not\in E(G)$ , wu, or $wv\not\in E(G)\}\geq n+1$ , then G is weakly vertex-pancyclic. This result also implies a conjecture of Faudree et al.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Oct 5, 2008

There are no references for this article.