The Generalized Connectivity of (n,k)-Bubble-Sort Graphs

For a vertex set [Formula: see text] of [Formula: see text], we use [Formula: see text] to denote the maximum number of edge-disjoint Steiner trees of [Formula: see text] such that any two of such trees intersect in [Formula: see text]. The generalized [Formula: see text]-connectivity of [Formula: see text] is defined as [Formula: see text]. We get that for any generalized Petersen graph [Formula: see text] with [Formula: see text], [Formula: see text] when [Formula: see text]. We give the values of [Formula: see text] for Petersen graph [Formula: see text], where [Formula: see text], and the values of [Formula: see text] for generalized Petersen graph [Formula: see text], where [Formula: see text] and [Formula: see text].

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A passivity-based decentralized strategy for generalized connectivity maintenance

The International Journal of Robotics Research ◽

10.1177/0278364912469671 ◽

2013 ◽

Vol 32 (3) ◽

pp. 299-323 ◽

Cited By ~ 68

Author(s):

Paolo Robuffo Giordano ◽

Antonio Franchi ◽

Cristian Secchi ◽

Heinrich H Bülthoff

Keyword(s):

Generalized Connectivity ◽

Connectivity Maintenance

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On generalized 3-connectivity of the strong product of graphs

Applicable Analysis and Discrete Mathematics ◽

10.2298/aadm160726003a ◽

2018 ◽

Vol 12 (2) ◽

pp. 297-317

Author(s):

Encarnación Abajo ◽

Rocío Casablanca ◽

Ana Diánez ◽

Pedro García-Vázquez

Keyword(s):

Positive Integer ◽

Connected Graph ◽

Sharp Bound ◽

Connected Graphs ◽

Strong Product ◽

Generalized Connectivity ◽

Internally Disjoint Trees ◽

Product Of Graphs

Let G be a connected graph with n vertices and let k be an integer such that 2 ? k ? n. The generalized connectivity kk(G) of G is the greatest positive integer l for which G contains at least l internally disjoint trees connecting S for any set S ? V (G) of k vertices. We focus on the generalized connectivity of the strong product G1 _ G2 of connected graphs G1 and G2 with at least three vertices and girth at least five, and we prove the sharp bound k3(G1 _ G2) ? k3(G1)_3(G2) + k3(G1) + k3(G2)-1.

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