scholarly journals RETRACTED: Pancyclic graphs and degree sum and neighborhood union involving distance two

2012 ◽  
Vol 160 (3) ◽  
pp. 218-223
Author(s):  
Kewen Zhao
Keyword(s):  
Degree Sum ◽  
Pancyclic Graphs ◽  
Neighborhood Union

Vertex Pancyclic Graphs

1999 ◽  
Vol 3 ◽  
pp. 166-170
Author(s):  
Bert Randerath ◽  
Lutz Volkmann ◽  
Ingo Schiermeyer ◽  
Meike Tewes
Keyword(s):  
Pancyclic Graphs

scholarly journals Degree and neighborhood intersection conditions restricted to induced subgraphs ensuring Hamiltonicity of graphs

2014 ◽  
Vol 06 (03) ◽  
pp. 1450043
Author(s):  
Bo Ning ◽  
Shenggui Zhang ◽  
Bing Chen
Keyword(s):  
Hamilton Cycles ◽  
Induced Subgraphs ◽  
Degree Sum ◽  
Degree Condition

Let claw be the graph K1,3. A graph G on n ≥ 3 vertices is called o-heavy if each induced claw of G has a pair of end-vertices with degree sum at least n, and called 1-heavy if at least one end-vertex of each induced claw of G has degree at least n/2. In this note, we show that every 2-connected o-heavy or 3-connected 1-heavy graph is Hamiltonian if we restrict Fan-type degree condition or neighborhood intersection condition to certain pairs of vertices in some small induced subgraphs of the graph. Our results improve or extend previous results of Broersma et al., Chen et al., Fan, Goodman and Hedetniemi, Gould and Jacobson, and Shi on the existence of Hamilton cycles in graphs.

scholarly journals Nonhamiltonian 2-connected claw-free graphs with large 4-degree sum

2001 ◽  
Vol 236 (1-3) ◽  
pp. 123-130 ◽  
Author(s):  
Wacław Frydrych
Keyword(s):  
Degree Sum

scholarly journals Pancyclic graphs II

1976 ◽  
Vol 20 (1) ◽  
pp. 41-46 ◽  
Author(s):  
J.A Bondy ◽  
A.W Ingleton
Keyword(s):  
Pancyclic Graphs

scholarly journals Degree sum conditions for the circumference of 4-connected graphs

2014 ◽  
Vol 333 ◽  
pp. 66-83
Author(s):  
Shuya Chiba ◽  
Masao Tsugaki ◽  
Tomoki Yamashita
Keyword(s):  
Connected Graphs ◽  
Degree Sum

GENERA OF THE LINKS DERIVED FROM 2-CONNECTED PLANE GRAPHS

2012 ◽  
Vol 21 (14) ◽  
pp. 1250129 ◽  
Author(s):  
SHUYA LIU ◽  
HEPING ZHANG
Keyword(s):  
Explicit Formula ◽  
Large Family ◽  
Plane Graph ◽  
Plane Graphs ◽  
Degree Sum ◽  
Oriented Link

In this paper, we associate a plane graph G with an oriented link by replacing each vertex of G with a special oriented n-tangle diagram. It is shown that such an oriented link has the minimum genus over all orientations of its unoriented version if its associated plane graph G is 2-connected. As a result, the genera of a large family of unoriented links are determined by an explicit formula in terms of their component numbers and the degree sum of their associated plane graphs.

scholarly journals (2)-pancyclic graphs

2013 ◽  
Vol 161 (7-8) ◽  
pp. 1128-1136 ◽  
Author(s):  
Carol T. Zamfirescu
Keyword(s):  
Pancyclic Graphs

Some Results on Degree Sum Energy of a Graph

2020 ◽  
pp. 353-359
Author(s):  
Mitesh J. Patel ◽  
G. V. Ghodasara
Keyword(s):  
Degree Sum
Sign in / Sign up

Export Citation Format

Share Document