Hamiltonian Spectra of Graphs

A hamiltonian walk in a digraph D is a closed spanning directed walk of D with minimum length. The length of a hamiltonian walk in D is called the hamiltonian number of D , and is denoted by h ( D ). The hamiltonian spectrum S h ( G ) of a graph G is the set { h ( D ) : D is a strongly connected ori...

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Bibliographic Details
Published inGraphs and combinatorics Vol. 35; no. 4; pp. 827 - 836
Main Authors Tong, Li-Da, Yang, Hao-Yu, Zhu, Xuding
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.07.2019
Springer Nature B.V
Subjects
Combinatorics
Engineering Design
Graph theory
Graphs
Integers
Mathematics
Mathematics and Statistics
Original Paper
Hamiltonian spectrum
05C45
Orientation
05C69
Hamiltonian number
05C38
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Summary:A hamiltonian walk in a digraph D is a closed spanning directed walk of D with minimum length. The length of a hamiltonian walk in D is called the hamiltonian number of D , and is denoted by h ( D ). The hamiltonian spectrum S h ( G ) of a graph G is the set { h ( D ) : D is a strongly connected orientation of G } . In this paper, we present necessary and sufficient conditions for a graph G of order n to have S h ( G ) = { n } , { n + 1 } , or { n + 2 } . Then we construct some 2-connected graphs of order n with hamiltonian spectrum being a singleton n + k for some k ≥ 3 , and graphs with their hamiltonian spectra being sets of consecutive integers.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-019-02035-0