Girth tenacity of some cube-like networks.
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| Title: | Girth tenacity of some cube-like networks. |
|---|---|
| Authors: | Yang, Yuxing1 (AUTHOR) yyx@htu.edu.cn, Li, Jing1,2 (AUTHOR) jing-li83@hotmail.com, Zhao, Shu-Li1 (AUTHOR) |
| Source: | Discrete Applied Mathematics. Oct2026, Vol. 391, p114-121. 8p. |
| Subjects: | Graph theory, Hypercubes, Hypercube networks (Computer networks) |
| Abstract: | The girth vertex (resp. edge) tenacity g τ v (G) (resp. g τ e (G)) of a non-acyclic simple graph G is defined to be the maximum number k such that the removal of any k vertices (resp. edges) of G does not change its girth. In this paper, we mainly investigated the girth tenacity of the exchanged hypercube E H (s , t) with s , t ≥ 1 , the ternary n -cube Q n 3 and the exchanged ternary n -cube E 3 C (r , s , t) with n = r + s + t and r , s , t ≥ 0. We proved that (i) g τ v (E H (1 , 1)) = 0 , g τ v (E H (s , t)) = 2 ⌊ 2 t + 1 3 ⌋ − 1 for s = 1 and t ≥ 2 , g τ v (E H (s , t)) = 2 ⌊ 2 s + 1 3 ⌋ − 1 for t = 1 and s ≥ 2 , g τ v (E H (s , t)) = ⌊ 2 t + 1 3 ⌋ 2 s + ⌊ 2 s + 1 3 ⌋ 2 t − 1 for min { s , t } ≥ 2 , and (i i) g τ v (Q n 3) = 3 n − 1 − 1 , g τ e (Q n 3) = n 3 n − 1 − 1 , and (i i i) g τ v (E 3 C (r , s , t)) = 3 n − 1 − 1 , g τ e (E 3 C (r , s , t)) = (n + 2) 3 n − 2 − 1. Some results on the girth tenacity of the hypercube were also listed. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 194551714 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Girth tenacity of some cube-like networks. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Yang%2C+Yuxing%22">Yang, Yuxing</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> yyx@htu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Jing%22">Li, Jing</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> jing-li83@hotmail.com</i><br /><searchLink fieldCode="AR" term="%22Zhao%2C+Shu-Li%22">Zhao, Shu-Li</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Oct2026, Vol. 391, p114-121. 8p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Hypercubes%22">Hypercubes</searchLink><br /><searchLink fieldCode="DE" term="%22Hypercube+networks+%28Computer+networks%29%22">Hypercube networks (Computer networks)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The girth vertex (resp. edge) tenacity g τ v (G) (resp. g τ e (G)) of a non-acyclic simple graph G is defined to be the maximum number k such that the removal of any k vertices (resp. edges) of G does not change its girth. In this paper, we mainly investigated the girth tenacity of the exchanged hypercube E H (s , t) with s , t ≥ 1 , the ternary n -cube Q n 3 and the exchanged ternary n -cube E 3 C (r , s , t) with n = r + s + t and r , s , t ≥ 0. We proved that (i) g τ v (E H (1 , 1)) = 0 , g τ v (E H (s , t)) = 2 ⌊ 2 t + 1 3 ⌋ − 1 for s = 1 and t ≥ 2 , g τ v (E H (s , t)) = 2 ⌊ 2 s + 1 3 ⌋ − 1 for t = 1 and s ≥ 2 , g τ v (E H (s , t)) = ⌊ 2 t + 1 3 ⌋ 2 s + ⌊ 2 s + 1 3 ⌋ 2 t − 1 for min { s , t } ≥ 2 , and (i i) g τ v (Q n 3) = 3 n − 1 − 1 , g τ e (Q n 3) = n 3 n − 1 − 1 , and (i i i) g τ v (E 3 C (r , s , t)) = 3 n − 1 − 1 , g τ e (E 3 C (r , s , t)) = (n + 2) 3 n − 2 − 1. Some results on the girth tenacity of the hypercube were also listed. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.dam.2026.04.037 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 8 StartPage: 114 Subjects: – SubjectFull: Graph theory Type: general – SubjectFull: Hypercubes Type: general – SubjectFull: Hypercube networks (Computer networks) Type: general Titles: – TitleFull: Girth tenacity of some cube-like networks. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Yang, Yuxing – PersonEntity: Name: NameFull: Li, Jing – PersonEntity: Name: NameFull: Zhao, Shu-Li IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 10 Text: Oct2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0166218X Numbering: – Type: volume Value: 391 Titles: – TitleFull: Discrete Applied Mathematics Type: main |
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