Hamiltonian properties of generalized Halin graphs. (English) Zbl 1171.05031

Malik, Shabnam; Qureshi, Ahmad Mahmood; Zamfirescu, Tudor

Can. Math. Bull. 52, No. 3, 416-423 (2009).

Summary: 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.

MSC:

05C45	Eulerian and Hamiltonian graphs
05C38	Paths and cycles

Keywords:

\(k\)-Halin graph; Hamiltonian; Hamiltonian connected; traceable