Advertisement
Published in:
2011 | OriginalPaper | Chapter
Hamiltonian of Line Graph under Condition of Constraint
Author : Yong-Zhi Kan
Published in: Informatics in Control, Automation and Robotics
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
In this paper, a
D
-closed trail problem for a class of the graph
G
under condition of constraint is discussed. We prove line graph
L
(
G
) of
G
is a Hamiltonian graph by using the method of induced sub-graph’s degree analysis. The main result of this paper is that let
G
be a simple connected, almost bridgeless graph of order
n
≥3,
G
≠
K
1,n − 1
,
Q
1
and
Q
2
, if
d
(
I
)≥2n-6 for each induced sub-graph
I
isomorphic to
P
4
, then,
G
has a
D
-closed trail. Accordingly, line graph
L
(
G
) of
G
is a Hamiltonian graph.