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The size of graphs uniquely hamiltonian-connected from a vertex

✍ Scribed by G.R.T Hendry

Publisher: Elsevier Science
Year: 1986
Tongue: English
Weight: 220 KB
Volume: 61
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(86)90027-0

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✦ Synopsis

A graph G is called uniquely hamiltonian-connected from a vertex v of G if G contains exactly one v-u hamiltonian path for each vertex u, u ~ v. It is shown that if G is uniquely hamiltonian-connected from a vertex v and G has order n/> 5, then G has exactly ½(3n-3) edges, G -v has exactly one hamiltonian cycle, every neighbour of v has degree 3 and every other vertex has degree at most 4.

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