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Title: The upper traceable number of a graph (English)
Author: Okamoto, Futaba
Author: Zhang, Ping
Author: Saenpholphat, Varaporn
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 1
Year: 2008
Pages: 271-287
Summary lang: English
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Category: math
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Summary: For a nontrivial connected graph $G$ of order $n$ and a linear ordering $s\: v_1, v_2, \ldots , v_n$ of vertices of $G$, define $d(s) = \sum _{i=1}^{n-1} d(v_i, v_{i+1})$. The traceable number $t(G)$ of a graph $G$ is $t(G) = \min \lbrace d(s)\rbrace $ and the upper traceable number $t^+(G)$ of $G$ is $t^+(G) = \max \lbrace d(s)\rbrace ,$ where the minimum and maximum are taken over all linear orderings $s$ of vertices of $G$. We study upper traceable numbers of several classes of graphs and the relationship between the traceable number and upper traceable number of a graph. All connected graphs $G$ for which $t^+(G)- t(G) = 1$ are characterized and a formula for the upper traceable number of a tree is established. (English)
Keyword: traceable number
Keyword: upper traceable number
Keyword: Hamiltonian number
MSC: 05C12
MSC: 05C45
idZBL: Zbl 1174.05040
idMR: MR2402537
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Date available: 2009-09-24T11:54:48Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/128257
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