## 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

### Keywords:

$$k$$-Halin graph; Hamiltonian; Hamiltonian connected; traceable
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