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On the unitary Cayley graph of a finite ring.

Akhtar, Reza, Boggess, Megan, Jackson-Henderson, Tiffany, Jiménez, Isidora, Karpman, Rachel, Kinzel, Amanda, Pritikin, Dan (2009)

The Electronic Journal of Combinatorics [electronic only]

On Vertices Enforcing a Hamiltonian Cycle

Igor Fabrici, Erhard Hexel, Stanislav Jendrol’ (2013)

Discussiones Mathematicae Graph Theory

A nonempty vertex set X ⊆ V (G) of a hamiltonian graph G is called an H-force set of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian. The H-force number h(G) of a graph G is defined to be the smallest cardinality of an H-force set of G. In the paper the study of this parameter is introduced and its value or a lower bound for outerplanar graphs, planar graphs, k-connected graphs and prisms over graphs is determined.

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