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Edgeconnectivity augmentations of graphs and hypergraphs
"... A. Frank (Augmenting graphs to meet edgeconnectivity requirements, ..."
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A. Frank (Augmenting graphs to meet edgeconnectivity requirements,
The restricted edgeconnectivity of Kautz undirected graphs
 Ars Combin
, 2006
"... A connected graph is said to be super edgeconnected if every minimum edgecut isolates a vertex. The restricted edgeconnectivity λ ′ of a connected graph is the minimum number of edges whose deletion results in a disconnected graph such that each connected component has at least two vertices. A gr ..."
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graph G is called λ ′optimal if λ ′ (G) = min{dG(u) + dG(v) − 2: uv is an edge in G}. This paper proves that for any d and n with d ≥ 2 and n ≥ 1 the Kautz undirected graph UK(d, n) is λ ′optimal except UK(2, 1) and UK(2, 2) and, hence, is super edgeconnected except UK(2, 2). Keywords: Edgeconnectivity
The Restricted EdgeConnectivity of de Bruijn Undirected Graphs ∗
"... A connected graph is said to be super edgeconnected if every minimum edgecut isolates a vertex. The restricted edgeconnectivity λ ′ of a connected graph is the minimum number of edges whose deletion results in a disconnected graph such that each component has at least two vertices. It has been sh ..."
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is called λ ′optimal if λ ′ (G) = ξ(G). This paper proves that the de Bruijn undirected graph UB(d, n) is λ ′optimal except UB(2, 1), UB(3, 1) and UB(2, 3) and, hence, is super edgeconnected for n ≥ 1 and d ≥ 2. Keywords: Edgeconnectivity, Restricted edgeconnectivity, Super edgeconnected, de Bruijn
Restricted EdgeConnectivity of de Bruijn Digraphs
"... The restricted edgeconnectivity of a graph is an important parameter to measure faulttolerance of interconnection networks. This paper determines that the restricted edgeconnectivity of the de Bruijn digraph B(d, n) is equal to 2d − 2 for d ≥ 2 and n ≥ 2 except B(2, 2). As consequences, the supe ..."
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The restricted edgeconnectivity of a graph is an important parameter to measure faulttolerance of interconnection networks. This paper determines that the restricted edgeconnectivity of the de Bruijn digraph B(d, n) is equal to 2d − 2 for d ≥ 2 and n ≥ 2 except B(2, 2). As conse
Sufficient Conditions for a Graph to be Super Restricted EdgeConnected
"... Restricted edge connectivity is a more refined network reliability index than edge connectivity. A restricted edge cut F of a connected graph G is an edge cut such that G−F has no isolated vertex. The restricted edge connectivity λ ′ is theminimumcardinality over all restricted edge cuts.WecallG λ′ ..."
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condition for nonsuper restricted edgeconnected graphs with minimum degree δ ≥ 3 and D ≤ g − 2. Next, we prove that a connected graph with minimum degree δ ≥ 3 and D ≤ g −3 is super restricted edgeconnected. Finally, we give some sufficient conditions on the conditional diameter and the girth for super
On super edgeconnectivity of Cartesian product graphs
 NETWORKS, VOL. 49(2), 152–157
, 2007
"... The super edgeconnectivity λ ′ of a connected graph G is the minimum cardinality of an edgecut F in G such that every component of G − F contains at least two vertices. Let Gi be a connected graph with order ni, minimum degree δi and edgeconnectivity λi for i = 1, 2. This article shows that λ′(G ..."
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The super edgeconnectivity λ ′ of a connected graph G is the minimum cardinality of an edgecut F in G such that every component of G − F contains at least two vertices. Let Gi be a connected graph with order ni, minimum degree δi and edgeconnectivity λi for i = 1, 2. This article shows that λ
All 4EdgeConnected HHDFree Graphs are Z3Connected
"... An undirected graph G = (V, E) is called Z3connected if for all b: V → Z3 with P v∈V b(v) = 0, an orientation D = (V, A) of G has a Z3valued nowherezero flow f: A → Z3 − {0} such that P e∈δ+(v) f(e) − P e∈δ−(v) f(e) = b(v) for all v ∈ V. We show that all 4edgeconnected HHDfree graphs are Z3 ..."
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An undirected graph G = (V, E) is called Z3connected if for all b: V → Z3 with P v∈V b(v) = 0, an orientation D = (V, A) of G has a Z3valued nowherezero flow f: A → Z3 − {0} such that P e∈δ+(v) f(e) − P e∈δ−(v) f(e) = b(v) for all v ∈ V. We show that all 4edgeconnected HHDfree graphs are Z3
Results 1  10
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109,988