The super connectivity of exchanged crossed cube

The (s+t+1)-dimensional exchanged crossed cube, denoted by ECQ(s, t), proposed by Li et al., combines the advantages of the hypercube and the crossed cube. It has been proven that ECQ(s, t) has better properties than the fundamental hypercube in the aspects of the fewer edges, lower cost factor and smaller diameter. This paper studies the embedding of cycles in ECQ(s, t). It is proved that ECQ(s, t) contains an l-cycle of every length l from 4 to 2s+t+1 except that ECQ(2, 3) and ECQ(3, 3) do not contain a cycle of length 9 where [Formula: see text] and [Formula: see text]. This result reveals the fact that ECQ(s, t) nearly remains the cycle embedding capability, while it only has about half edges of crossed cube.

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Embedding a mesh of trees in the crossed cube

Information Processing Letters ◽

10.1016/j.ipl.2012.04.013 ◽

2012 ◽

Vol 112 (14-15) ◽

pp. 599-603 ◽

Cited By ~ 8

Author(s):

Qiang Dong ◽

Junlin Zhou ◽

Yan Fu ◽

Xiaofan Yang

Keyword(s):

Mesh Of Trees ◽

Crossed Cube

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Super connectivity of a family of direct product graphs

International Journal of Computer Mathematics Computer Systems Theory ◽

10.1080/23799927.2021.1974567 ◽

2021 ◽

pp. 1-5

Author(s):

F. Soliemany ◽

M. Ghasemi ◽

R. Varmazyar

Keyword(s):

Direct Product ◽

Product Graphs ◽

Super Connectivity

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Super Connectivity of Erdős-Rényi Graphs

Mathematics ◽

10.3390/math7030267 ◽

2019 ◽

Vol 7 (3) ◽

pp. 267 ◽

Cited By ~ 1

Author(s):

Yilun Shang

Keyword(s):

Random Graphs ◽

Minimum Cardinality ◽

Super Connectivity ◽

Isolated Vertex ◽

Disconnected Graph

The super connectivity κ ′ ( G ) of a graph G is the minimum cardinality of vertices, if any, whose deletion results in a disconnected graph that contains no isolated vertex. G is said to be r-super connected if κ ′ ( G ) ≥ r . In this note, we establish some asymptotic almost sure results on r-super connectedness for classical Erdős–Rényi random graphs as the number of nodes tends to infinity. The known results for r-connectedness are extended to r-super connectedness by pairing off vertices and estimating the probability of disconnecting the graph that one gets by identifying the two vertices of each pair.

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