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:

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

MSC Classifications:

05C45, 05C38 show english descriptions Eulerian and Hamiltonian graphs
Paths and cycles [See also 90B10] 05C45 - Eulerian and Hamiltonian graphs
05C38 - Paths and cycles [See also 90B10]

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