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228
On the Connectivity and Superconnectivity of Bipartite Digraphs and Graphs
"... In this work, first, we present sufficient conditions for a bipartite digraph to attain optimum values of a stronger measure of connectivity, the socalled superconnectivity. To be more precise, we study the problem of disconnecting a maximally connected bipartite (di)graph by removing nontrivial su ..."
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Cited by 6 (2 self)
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subsets of vertices or edges. Within this framework, both an upperbound on the diameter and Chartrand type conditions to guarantee optimum superconnectivities are obtained. Secondly, we show that if the order or size of a bipartite (di)graph is small enough then its vertex connectivity or edgeconnectivity
Super connectivity of regular graphs with small diameter
"... A graph is superconnected, for short superκ, if all minimum vertexcuts consist of the vertices adjacent with one vertex. In this paper we prove for any rregular graph of diameter D and odd girth g that if D ≤ g − 2, then the graph is superκ when g ≥ 5 and a complete graph otherwise. ..."
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Cited by 1 (0 self)
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A graph is superconnected, for short superκ, if all minimum vertexcuts consist of the vertices adjacent with one vertex. In this paper we prove for any rregular graph of diameter D and odd girth g that if D ≤ g − 2, then the graph is superκ when g ≥ 5 and a complete graph otherwise.
An open problem: (4; g)cages with odd g ≥ 5 are tightly superconnected
"... Interconnection networks form an important area which has received much attention, both in theoretical research and in practice. From theoretical point of view, an interconnection network can be modelled by a graph, where the vertices of the graph represent the nodes of the network and the edges o ..."
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vertices of G. We say that G is tconnected if the deletion of at least t vertices of G is required to disconnect the graph. A graph with minimum degree δ is maximally connected if it is δconnected. A graph is superconnected if its only minimum disconnecting sets are those induced by the neighbors of a
On Superconnectivity of (4, g)Cages with Even Girth
"... A (k, g)cage is a kregular graph with girth g that has the fewest number of vertices. It has been conjectured [Fu, Huang, and Rodger, Connectivity of cages, J. Graph Theory 24 (1997), 187191] that all (k, g)cages are kconnected for k ≥ 3. A connected graph G is said to be superconnected if ever ..."
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A (k, g)cage is a kregular graph with girth g that has the fewest number of vertices. It has been conjectured [Fu, Huang, and Rodger, Connectivity of cages, J. Graph Theory 24 (1997), 187191] that all (k, g)cages are kconnected for k ≥ 3. A connected graph G is said to be superconnected
Cayley Graphs and Interconnection Networks
, 1997
"... In this report, we will focus on routing problems including connectivity, diameter and loads of routings. We place the emphasis on load problems, since new classes of vertextransitive graphs (see quasiCayley graphs in Section 5.3) or edgetransitive graphs (see regular orbital graphs in Section 5. ..."
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Cited by 72 (3 self)
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In this report, we will focus on routing problems including connectivity, diameter and loads of routings. We place the emphasis on load problems, since new classes of vertextransitive graphs (see quasiCayley graphs in Section 5.3) or edgetransitive graphs (see regular orbital graphs in Section 5
CONNECTIVITY OF PATH GRAPHS
, 2003
"... The aim of this paper is to lower bound the connectivity of kpath graphs. From the bounds obtained, we give conditions to guarantee maximum connectivity. Then, it is shown that those maximally connected graphs satisfying the previous conditions are also superlambda. While doing so, we derive some ..."
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Cited by 1 (0 self)
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The aim of this paper is to lower bound the connectivity of kpath graphs. From the bounds obtained, we give conditions to guarantee maximum connectivity. Then, it is shown that those maximally connected graphs satisfying the previous conditions are also superlambda. While doing so, we derive
On the order and size of sgeodetic digraphs with given connectivity
 DISCRETE MATHEMATICS
, 1997
"... A digraph G = (V, E) with diameter D is said to be sgeodetic, for 1 ≤ s ≤ D, if between any pair of (not necessarily different) vertices x, y ∈ V there is at most one x → y path of length ≤ s. Thus, any loopless digraph is at least 1geodetic. A similar definition applies for a graph G, but in this ..."
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Cited by 3 (1 self)
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maximum value. In other words, the (di)graph is maximally connected. Moreover, a similar result involving the size m (number of edges) and edgeconnectivity applies. In this work we mainly show that the same conclusions can be reached if the order or size of a sgeodetic (di)graph is small enough. As a
The (α, β,s, t)diameter of graphs: A particular case of conditional diameter
, 2006
"... The conditional diameter of a connected graph Γ = (V,E) is defined as follows: given a property P of a pair (Γ1,Γ2) of subgraphs of Γ, the socalled conditional diameter or Pdiameter measures the maximum distance among subgraphs satisfying P. That is, DP(Γ): = max Γ1,Γ2⊂Γ {∂(Γ1,Γ2) : Γ1,Γ2 satisfy ..."
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The conditional diameter of a connected graph Γ = (V,E) is defined as follows: given a property P of a pair (Γ1,Γ2) of subgraphs of Γ, the socalled conditional diameter or Pdiameter measures the maximum distance among subgraphs satisfying P. That is, DP(Γ): = max Γ1,Γ2⊂Γ {∂(Γ1,Γ2) : Γ1,Γ2 satisfy
Results 1  10
of
228