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Hamiltonian Properties of Generalized Halin Graphs

Published online by Cambridge University Press:  20 November 2018

Shabnam Malik ,
Ahmad Mahmood Qureshi  and
Tudor Zamfirescu
Shabnam Malik
Affiliation:
Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan e-mail: shabnam.malik@gmail.comsirahmad@gmail.com
Ahmad Mahmood Qureshi
Affiliation:
Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan e-mail: shabnam.malik@gmail.comsirahmad@gmail.com
Tudor Zamfirescu
Affiliation:
Faculty of Mathematics, University of Dortmund, 44221 Dortmund, Germany, and , Institute of Mathematics, Romanian Academy, Bucharest, Romania e-mail: tzamfirescu@yahoo.com
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Abstract

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A Halin graph is a graph $H\,=\,T\,\cup \,C$, where $T$ is a tree with no vertex of degree two, and $C$ is a cycle connecting the end-vertices of $T$ in the cyclic order determined by a plane embedding of $T$. In this paper, we define classes of generalized Halin graphs, called $k$-Halin graphs, and investigate their Hamiltonian properties.

Keywords

05C4505C38k-Halin GraphHamiltonianHamiltonian connectedtraceable
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 3 , 01 September 2009 , pp. 416 - 423
Copyright
Copyright © Canadian Mathematical Society 2009

References

[1] Barefoot, C. A., Hamiltonian connectivity of the Halin graphs. Congr. Numer. 58(1987) 93–102.Google Scholar
[2] Bondy, J. A., Pancyclic graphs: recent results. In: Infinite and Finite Sets. Colloq. Math. Soc. János Bolyai 10, North-Holland, Amsterdam, 1975, pp. 181–187.Google Scholar
[3] Bondy, J. A. and Lovász, L., Lengths of cycles in Halin graphs. J. Graph Theory 9(1985) 397–410.Google Scholar
[4] Lovász, L. and Plummer, M. D., On a family of planar bicritical graphs. Proc. London Math. Soc. 30(1975) 160–176.Google Scholar
[5] Malkevitch, J., Cycle lengths in polytopal graphs. In: Theory and Applications of Graphs, Lectures Notes in Math. 642. Springer Berlin. 1978 pp. 364–370.Google Scholar
[6] Skowrońska, M., The pancyclicity of Halin graphs and their exterior contractions, In: Cycles in Graphs, North-Holland Math. Stud. 115. North-Holland, Amsterdam, 1985, pp. 179–194.Google Scholar