The generalized 4-connectivity of a family of regular graphs.

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος:	The generalized 4-connectivity of a family of regular graphs.
Συγγραφείς:	Zhao, Shu-Li¹ (AUTHOR) zhaoshuli0210@126.com, Zhang, Bao-Cheng¹ (AUTHOR)
Πηγή:	Discrete Applied Mathematics. Dec2026, Vol. 394, p115-126. 12p.
Θεματικοί όροι:	Regular graphs, Star graphs (Graph theory), Computer network reliability, Fault tolerance (Engineering), *Spanning trees
Περίληψη:	Let G be a connected graph and S ⊆ V (G) with \| S \| ≥ 2. A tree T in G is called an S -tree if S ⊆ V (T). Two S -trees T 1 and T 2 are called internally disjoint if E (T 1) ∩ E (T 2) = 0̸ and V (T 1) ∩ V (T 2) = S. For an integer k with 2 ≤ k ≤ n , the generalized k -connectivity of a graph G is defined as κ k (G) = min { κ G (S) \| S ⊆ V (G) and \| S \| = k } , where κ G (S) denotes the maximum number of internally disjoint S -trees in G. The generalized k -connectivity extends traditional connectivity and serves as a crucial measure for evaluating the reliability and fault tolerance of connecting any k vertices in G. In this paper, we mainly investigate the generalized 4-connectivity of a family of regular graph G n , which improves the known results about generalized 3-connectivity of G n in Zhao et al., (2021). For a reason that the alternating group network A N n , the star graph S n and pancake graphs P n are special cases of the regular graph G n , as applications of the main result, we obtain that κ 4 (A N n) = n − 2 for n ≥ 4 , κ 4 (S n) = n − 2 for n ≥ 3 and κ 4 (P n) = n − 2 for n ≥ 3. [ABSTRACT FROM AUTHOR]
Βάση Δεδομένων:	Academic Search Index

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Items	– Name: Title Label: Title Group: Ti Data: The generalized 4-connectivity of a family of regular graphs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhao%2C+Shu-Li%22">Zhao, Shu-Li</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhaoshuli0210@126.com</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Bao-Cheng%22">Zhang, Bao-Cheng</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Dec2026, Vol. 394, p115-126. 12p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Regular+graphs%22">Regular graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Star+graphs+%28Graph+theory%29%22">Star graphs (Graph theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+network+reliability%22">Computer network reliability</searchLink><br /><searchLink fieldCode="DE" term="%22Fault+tolerance+%28Engineering%29%22">Fault tolerance (Engineering)</searchLink><br />*<searchLink fieldCode="DE" term="%22Spanning+trees%22">Spanning trees</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Let G be a connected graph and S ⊆ V (G) with \| S \| ≥ 2. A tree T in G is called an S -tree if S ⊆ V (T). Two S -trees T 1 and T 2 are called internally disjoint if E (T 1) ∩ E (T 2) = 0̸ and V (T 1) ∩ V (T 2) = S. For an integer k with 2 ≤ k ≤ n , the generalized k -connectivity of a graph G is defined as κ k (G) = min { κ G (S) \| S ⊆ V (G) and \| S \| = k } , where κ G (S) denotes the maximum number of internally disjoint S -trees in G. The generalized k -connectivity extends traditional connectivity and serves as a crucial measure for evaluating the reliability and fault tolerance of connecting any k vertices in G. In this paper, we mainly investigate the generalized 4-connectivity of a family of regular graph G n , which improves the known results about generalized 3-connectivity of G n in Zhao et al., (2021). For a reason that the alternating group network A N n , the star graph S n and pancake graphs P n are special cases of the regular graph G n , as applications of the main result, we obtain that κ 4 (A N n) = n − 2 for n ≥ 4 , κ 4 (S n) = n − 2 for n ≥ 3 and κ 4 (P n) = n − 2 for n ≥ 3. [ABSTRACT FROM AUTHOR]
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RecordInfo	BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.dam.2026.07.024 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 115 Subjects: – SubjectFull: Regular graphs Type: general – SubjectFull: Star graphs (Graph theory) Type: general – SubjectFull: Computer network reliability Type: general – SubjectFull: Fault tolerance (Engineering) Type: general – SubjectFull: Spanning trees Type: general Titles: – TitleFull: The generalized 4-connectivity of a family of regular graphs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhao, Shu-Li – PersonEntity: Name: NameFull: Zhang, Bao-Cheng IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 12 Text: Dec2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0166218X Numbering: – Type: volume Value: 394 Titles: – TitleFull: Discrete Applied Mathematics Type: main
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