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A census of maximum uniquely hamiltonian graphs

✍ Scribed by Curtiss A. Barefoot; R. C. Entringer


Publisher
John Wiley and Sons
Year
1981
Tongue
English
Weight
261 KB
Volume
5
Category
Article
ISSN
0364-9024

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✦ Synopsis


Abstract

We show that there are 2^[n/2]‐4^ largest graphs of order n β‰₯ 7 having exactly one hamiltonian cycle. a recursive procedure for constructing these graphs is described.


πŸ“œ SIMILAR VOLUMES


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The hamiltonian path graph H(F) of a graph F is that graph having the same vertex set as F and in which two vertices u and u are adjacent if and only if F contains a hamiltonian u -u path. First, in response to a conjecture of Chartrand, Kapoor and Nordhaus, a characterization of nonhamiltonian grap

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## Abstract In this paper, we show that __n__ β©Ύ 4 and if __G__ is a 2‐connected graph with 2__n__ or 2__n__βˆ’1 vertices which is regular of degree __n__βˆ’2, then __G__ is Hamiltonian if and only if __G__ is not the Petersen graph.

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## Abstract We construct 3‐regular (cubic) graphs __G__ that have a dominating cycle __C__ such that no other cycle __C__~1~ of __G__ satisfies __V(C)__ βŠ† __V__(__C__~1~). By a similar construction we obtain loopless 4‐regular graphs having precisely one hamiltonian cycle. The basis for these const