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Theoretical Computer Science, ISSN 0304-3975, 01/2018, Volume 707, pp. 56 - 68
A connected graph G is called strongly Menger (edge) connected if for any two distinct vertices x,y of G, there are min⁡{degG⁡(x),degG⁡(y)}(-edge)-disjoint... 
Strong Menger (edge) connectivity | Fault-tolerance | Balanced hypercube | Maximal local-connectivity | g-Extra (edge) connectivity | STAR GRAPHS | AUGMENTED CUBES | NETWORKS | RELIABILITY | FOLDED HYPERCUBES | CONDITIONAL FAULTS | BIPANCYCLICITY | LOCAL-CONNECTIVITY | EXTRACONNECTIVITY | COMPUTER SCIENCE, THEORY & METHODS
Journal Article
by Guo, LT and Guo, XF
ARS COMBINATORIA, ISSN 0381-7032, 10/2016, Volume 129, pp. 165 - 172
Let G be a connected graph and k >= 1 be an integer. Local k-restricted edge connectivity lambda(k) (X, Y) of X, Y in G is the maximum number of the edge... 
MATHEMATICS | Local restricted edge connectivity | Restricted edge connectivity
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 06/2018, Volume 728, pp. 1 - 8
Menger's theorem is a characterization of the connectivity in finite graphs in terms of the minimum number of disjoint paths that can be found between any pair... 
Hypercubes | Folded hypercubes | Connectivity | Strong Menger connectivity | Fault-tolerance | Strong Menger edge connectivity | STAR GRAPHS | LOCAL-CONNECTIVITY | COMPUTER SCIENCE, THEORY & METHODS | FAULTS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 04/2019, Volume 259, pp. 145 - 152
From Menger’s theorem, a graph is k-connected if and only if there are at least k-internally disjoint paths between any two distinct vertices. Therefore, the... 
Connectivity | Hypercube-like networks | Fault-tolerance | Strong Menger edge connectivity | CONDITIONAL FAULTS | MATHEMATICS, APPLIED | PANCYCLICITY | BIPANCYCLICITY | LOCAL-CONNECTIVITY | FOLDED HYPERCUBES | Fault tolerance | Hypercubes | Dimensional tolerances | Graph theory | Apexes
Journal Article
Ars Combinatoria, ISSN 0381-7032, 2014, Volume 113, pp. 97 - 104
The local-restricted-edge-connectivity lambda'(e, f) of two nonadjacent edges e and f in graph G is the maximum number of edge-disjoint e-f paths in G. It is... 
Edge-degree | Restricted-edge-connectivity | Local-restricted-edge-connectivity | MATHEMATICS | SUFFICIENT CONDITIONS | DIGRAPHS | LAMBDA
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2009, Volume 157, Issue 4, pp. 691 - 698
For a graph G , a detachment operation at a vertex transforms the graph into a new graph by splitting the vertex into several vertices in such a way that the... 
Detachment | Eulerian graphs | Edge-splitting | Local edge-connectivity | MATHEMATICS, APPLIED | DIGRAPHS | GRAPHS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2008, Volume 156, Issue 7, pp. 1011 - 1018
Let G = ( V + s , E ) be a 2-edge-connected graph with a designated vertex s. A pair of edges rs , st is called admissible if splitting off these edges... 
Splitting off | Edge-connectivity augmentation | Local edge-connectivity | local edge-connectivity | MATHEMATICS, APPLIED | AUGMENTATION | edge-connectivity augmentation | splitting off | Algorithms | Management science
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2006, Volume 154, Issue 16, pp. 2307 - 2329
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2007, Volume 307, Issue 24, pp. 3207 - 3212
A digraph without any cycle of length two is called an oriented graph. The local-edge-connectivity λ ( u , v ) of two vertices u and v in a digraph or graph D... 
Edge-connectivity | Local-edge-connectivity | Minimum degree | Digraph | Oriented graph | MATHEMATICS | edge-connectivity | digraph | DEGREE SEQUENCE CONDITIONS | SUFFICIENT CONDITIONS | EQUALITY | minimum degree | local-edge-connectivity | oriented graph
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 01/2015, Volume 31, Issue 6, pp. 2231 - 2259
The maximum local connectivity was first introduced by Bollobs. The problem of determining the maximum number of edges in a graph with. = has been studied... 
Internally (edge-)disjoint trees | (Edge-)connectivity | generalized local (edge-)connectivity | Packing | Steiner tree | MATHEMATICS | MAXIMUM NUMBER | GENERALIZED CONNECTIVITY | 3-CONNECTIVITY | PATHS | PRODUCT GRAPHS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 08/2017, Volume 85, Issue 4, pp. 814 - 838
A graph G has maximal local edge‐connectivity k if the maximum number of edge‐disjoint paths between every pair of distinct vertices x and y is at most k. We... 
local connectivity | coloring | vertex degree | minimally k‐connected | Brooks’ theorem | local edge‐connectivity | local edge-connectivity | minimally k-connected | MATHEMATICS | Brooks' theorem | Computer Science | Discrete Mathematics
Journal Article
IEEE Transactions on Parallel and Distributed Systems, ISSN 1045-9219, 03/2020, Volume 31, Issue 3, pp. 647 - 662
The generalized hypercube (GH) is one key interconnection network with excellent topological properties. It contains many other interconnection topologies,... 
Fault tolerance | Program processors | Network topology | local diagnosis | disjoint path | Hypercubes | Routing | Topology | low cost | Exchanged generalized hypercube | PATHS | EXTRA CONNECTIVITY | DIGRAPHS | ARC FAULT-TOLERANCE | DIAGNOSABILITY | ENGINEERING, ELECTRICAL & ELECTRONIC | routing | EDGE-CONNECTIVITY | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | CARTESIAN PRODUCT
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 11/2015, Volume 31, Issue 6, pp. 2231 - 2259
The maximum local connectivity was first introduced by Bollobás. The problem of determining the maximum number of edges in a graph with $$\overline{\kappa }\le... 
Internally (edge-)disjoint trees | (Edge-)connectivity | Packing | Steiner tree | 05C40 | Mathematics | generalized local (edge-)connectivity | 05C70 | Engineering Design | Combinatorics | 05C35 | 05C05
Journal Article
Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 2006, Volume 24, pp. 173 - 180
A detachment operation transforms a given graph by splitting some vertices into several their copies while maintaining the original set of edges, whose end... 
detachment | graphs | edge-splitting | Eulerian | local-edge-connectivity
Journal Article
Concurrency and Computation: Practice and Experience, ISSN 1532-0626, 05/2019, Volume 31, Issue 10, pp. e4787 - n/a
Summary Suppose that G = (V(G), E(G)) is a connected graph and D(G) is the diameter of G. For two distinct vertices a1, b1 ∈ V, κ(a1, b1), defined as local... 
local connectivity | diameter | distance connectivity | path matrix | COMPUTER SCIENCE, SOFTWARE ENGINEERING | EDGE-CONNECTIVITY | RELIABILITY-ANALYSIS | LOCAL-CONNECTIVITY | COMPUTER SCIENCE, THEORY & METHODS | Integers | Eigenvalues | Fault tolerance | Connectivity | Graphs | Apexes
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 06/2013, Volume 489-490, pp. 67 - 74
We consider the Tree Augmentation problem: given a graph G=(V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F⊆E such that... 
Edge-connectivity | Tree Augmentation | Approximation algorithms | Laminar family | Local replacement | APPROXIMATION | COMPUTER SCIENCE, THEORY & METHODS | Algorithms
Journal Article
INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE, ISSN 0129-0541, 12/2019, Volume 30, Issue 8, pp. 1301 - 1315
An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively.... 
EDGE-CONNECTIVITY | fault-tolerance | KIND | HYPERCUBE | COMPONENT | COMPUTER SCIENCE, THEORY & METHODS | Strong Menger connectivity | Cayley graph | maximal local-connectivity | CONDITIONAL CONNECTIVITY | transposition generating graphs | STRONG MENGER-CONNECTIVITY
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2015, Volume 29, Issue 3, pp. 1764 - 1782
Journal Article
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