Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Benhcine, A., Clark, L., Kohlar, N., Veldman, H.J.: On Circuits and Pancyclic line graph. J. Graph Theory 3(10), 411–425 (1986)
Zhao, L.C., Liu, C.F.: A Sufficient Condition for Hamiltonian Line Graph. Applied Mathematics (1), 22–26 (1990)
Harary, F., St. Nash-Williams, C.J.A.: On euleriam and hamiltonian graph and line graph. Canada Math. Bull 8, 701–710 (1965)
Veldman, H.J.: A Result on Hamiltonian Line Graphs lnvolving Restrictions on lnduced Subgraphs. J. Graph Theory 12(3), 413–420 (1988)
Zhao, L.C., Liu, C.F., Wang, H.: Note on Hamiltonian Line Graph. Journal of Applied Mathematics 9(1), 17–20 (1986)
Clark, L.: On Hamiltonian line graph. J. Graph Theory 8(3), 303–307 (1984)
Zhao, L.C., Liu, C.F.: A Sufficient Condition for Hamiltonian Line Graph. Journal of Qufu Normal University 15(4), 15–20 (1989)
Liu, C.F.: On Hamiltonian Line Graph in Graph K3-Free. Journal of Shenyang Golden University 13(4), 383–386 (1994)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kan, YZ. (2011). Hamiltonian of Line Graph under Condition of Constraint. In: Tan, H. (eds) Informatics in Control, Automation and Robotics. Lecture Notes in Electrical Engineering, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25899-2_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-25899-2_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25898-5
Online ISBN: 978-3-642-25899-2
eBook Packages: EngineeringEngineering (R0)