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

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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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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A Distributed Depth First Search based Algorithm for Edge Connectivity Estimation

2020 16th International Conference on Network and Service Management (CNSM) ◽

10.23919/cnsm50824.2020.9269062 ◽

2020 ◽

Author(s):

Onur Ugurlu ◽

Vahid Khalilpour Akram ◽

Deniz Tursel Eliiyi

Keyword(s):

Edge Connectivity ◽

Depth First Search

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The Edge-Connectivity of Token Graphs

Graphs and Combinatorics ◽

10.1007/s00373-021-02301-0 ◽

2021 ◽

Vol 37 (3) ◽

pp. 1013-1023

Author(s):

J. Leaños ◽

Christophe Ndjatchi

Keyword(s):

Edge Connectivity

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Spectral Threshold for Extremal Cyclic Edge-Connectivity

Graphs and Combinatorics ◽

10.1007/s00373-021-02333-6 ◽

2021 ◽

Author(s):

Sinan G. Aksoy ◽

Mark Kempton ◽

Stephen J. Young

Keyword(s):

Edge Connectivity ◽

Cyclic Edge Connectivity

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AN EFFICIENT DISTRIBUTED ALGORITHM FOR 3-EDGE-CONNECTIVITY

International Journal of Foundations of Computer Science ◽

10.1142/s0129054106004042 ◽

2006 ◽

Vol 17 (03) ◽

pp. 677-701 ◽

Cited By ~ 4

Author(s):

YUNG H. TSIN

Keyword(s):

Distributed Algorithm ◽

Computer Network ◽

Connected Components ◽

Message Complexity ◽

Edge Connectivity ◽

Worst Case ◽

Dense Networks

A distributed algorithm for finding the cut-edges and the 3-edge-connected components of an asynchronous computer network is presented. For a network with n nodes and m links, the algorithm has worst-case [Formula: see text] time and O(m + nhT) message complexity, where hT < n. The algorithm is message optimal when [Formula: see text] which includes dense networks (i.e. m ∈ Θ(n2)). The previously best known distributed algorithm has a worst-case O(n3) time and message complexity.

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