The (n,k)-Modified-Bubble-Sort Graph: A Generalized Modified-Bubble-Sort Graph

International Journal of Foundations of Computer Science ◽

10.1142/s0129054121500258 ◽

2021 ◽

pp. 1-12

Author(s):

Mengyue Cao ◽

Tongtong Ding ◽

Min Xu

Keyword(s):

Hierarchical Structure ◽

Edge Connectivity ◽

Super Connectivity

In this paper, we present a new interconnection topology, called the[Formula: see text]-modified-bubble-sort graph, which is a generalization of the modified-bubble-sort graph. Additionally, we show many of its properties, such as its hierarchical structure, vertex transitivity, connectivity, edge-connectivity, super connectivity and super edge-connectivity. The [Formula: see text]-modified-bubble-sort graph presents more flexibility than the modified-bubble-sort graph in terms of its major design properties.

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Super-connectivity and super-edge-connectivity for some interconnection networks

Applied Mathematics and Computation ◽

10.1016/s0096-3003(02)00223-0 ◽

2003 ◽

Vol 140 (2-3) ◽

pp. 245-254 ◽

Cited By ~ 44

Author(s):

Y-Chuang Chen ◽

Jimmy J.M. Tan ◽

Lih-Hsing Hsu ◽

Shin-Shin Kao

Keyword(s):

Interconnection Networks ◽

Edge Connectivity ◽

Super Connectivity

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Super Connectivity and Super Edge Connectivity of the Mycielskian of a Graph

Graphs and Combinatorics ◽

10.1007/s00373-011-1032-3 ◽

2011 ◽

Vol 28 (2) ◽

pp. 143-147 ◽

Cited By ~ 8

Author(s):

Litao Guo ◽

Ruifang Liu ◽

Xiaofeng Guo

Keyword(s):

Edge Connectivity ◽

Super Connectivity

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A Note on Super Connectivity of the Bouwer Graph

Journal of Interconnection Networks ◽

10.1142/s0219265921420093 ◽

2021 ◽

pp. 2142009

Author(s):

Mei-Mei Gu ◽

Jou-Ming Chang

Keyword(s):

Reliability Measures ◽

Edge Connectivity ◽

Super Connectivity ◽

Vertex Transitive ◽

Almost All ◽

Edge Transitive ◽

Structure Properties

The Bouwer graph [Formula: see text], proposed in 1970, is defined for every triple [Formula: see text] of integers greater than [Formula: see text] with [Formula: see text]. It has many good properties, such as vertex-transitive and edge-transitive. Conder and Žitnik used a cycle-counting argument to prove that almost all of the Bouwer graphs are half-arc-transitive in 2016. In this paper, by exploring the structure properties of [Formula: see text], we investigate some reliability measures, including super connectivity and super-edge connectivity, and show that the super connectivity and super-edge connectivity of the Bouwer graph are both [Formula: see text] for [Formula: see text], [Formula: see text] and [Formula: see text].

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Relationships between hierarchical structure and properties in macromolecular systems

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100126950 ◽

1987 ◽

Vol 45 ◽

pp. 440-443

Author(s):

E. Baer

Keyword(s):

Uniaxial Tension ◽

Hierarchical Structure ◽

Inorganic Material ◽

Hierarchical Structures ◽

Bone Collagen ◽

Structure And Properties ◽

Connective Tissues ◽

Scale Level ◽

Fibrous Protein ◽

Macromolecular Systems

The most advanced macromolecular materials are found in plants and animals, and certainly the connective tissues in mammals are amongst the most advanced macromolecular composites known to mankind. The efficient use of collagen, a fibrous protein, in the design of both soft and hard connective tissues is worthy of comment. Very crudely, in bone collagen serves as a highly efficient binder for the inorganic hydroxyappatite which stiffens the structure. The interactions between the organic fiber of collagen and the inorganic material seem to occur at the nano (scale) level of organization. Epitatic crystallization of the inorganic phase on the fibers has been reported to give a highly anisotropic, stress responsive, structure. Soft connective tissues also have sophisticated oriented hierarchical structures. The collagen fibers are “glued” together by a highly hydrated gel-like proteoglycan matrix. One of the simplest structures of this type is tendon which functions primarily in uniaxial tension as a reinforced elastomeric cable between muscle and bone.

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