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

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
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