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981
Parsing English with a Link Grammar
, 1991
"... We define a new formal grammatical system called a link grammar . A sequence of words is in the language of a link grammar if there is a way to draw links between words in such a way that (1) the local requirements of each word are satisfied, (2) the links do not cross, and (3) the words form a conn ..."
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Cited by 437 (4 self)
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connected graph. We have encoded English grammar into such a system, and written a program (based on new algorithms) for efficiently parsing with a link grammar. The formalism is lexical and makes no explicit use of constituents and categories. The breadth of English phenomena that our system handles
On the Minimum Node Degree and Connectivity of a Wireless Multihop Network
 ACM MobiHoc
, 2002
"... This paper investigates two fundamental characteristics of a wireless multihop network: its minimum node degree and its k–connectivity. Both topology attributes depend on the spatial distribution of the nodes and their transmission range. Using typical modeling assumptions — a random uniform distri ..."
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Cited by 318 (4 self)
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.g., if they set the parameters in a network–level simulation of a mobile ad hoc network or if they design a wireless sensor network. Categories and Subject Descriptors C.2 [Computercommunication networks]: Network architecture and design—wireless communication, network communications, network topology; G.2.2
The Average Distance in a Random Graph with Given Expected Degrees
"... Random graph theory is used to examine the “smallworld phenomenon”– any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees, the average distance is almost surely of order log n / log ˜ d whe ..."
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Cited by 289 (13 self)
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Random graph theory is used to examine the “smallworld phenomenon”– any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees, the average distance is almost surely of order log n / log ˜ d
THE CONNECTIVITY OF A PARTICULAR GRAPH
, 1991
"... Let G be a graph with vertex set N = {1, 2, 3,...} and edge set E where {a, b) e E if and only if a 2 + b 2 = c 2 for some c in JV. From the standard parameterization of Pythagorean triples, it is easy to deduce that 1 and 2 are isolated vertices and that 3 and 4 together comprise a connected compon ..."
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Let G be a graph with vertex set N = {1, 2, 3,...} and edge set E where {a, b) e E if and only if a 2 + b 2 = c 2 for some c in JV. From the standard parameterization of Pythagorean triples, it is easy to deduce that 1 and 2 are isolated vertices and that 3 and 4 together comprise a connected
Cycles in 2connected graphs
, 2004
"... Let Gn be a class of graphs on n vertices.For an integer c, let ex(Gn,c) be the smallest integer such that if G is a graph in Gn with more than ex(Gn,c) edges, then G contains a cycle of length more than c.A classical result of Erdös and Gallai is that if Gn is the class of all simple graphs on n ve ..."
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Cited by 2 (0 self)
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, and conjectured that if Gn is the class of all 2connected simple graphs on n vertices, then ex(Gn,c) = max{f (n, 2, c), f (n, ⌊c/2⌋,c)}, c+1−t where f (n, t, c) = 2 + t(n − c − 1 + t),2�t �c/2, is the number of edges in the graph obtained from Kc+1−t by adding n − (c + 1 − t) isolated vertices each joined
Implementation of a Portable Nested DataParallel Language
 Journal of Parallel and Distributed Computing
, 1994
"... This paper gives an overview of the implementation of Nesl, a portable nested dataparallel language. This language and its implementation are the first to fully support nested data structures as well as nested dataparallel function calls. These features allow the concise description of parallel alg ..."
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Cited by 205 (28 self)
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. It runs on the Connection Machine CM2, the Cray YMP C90, and serial machines. We compare initial benchmark results of Nesl with those of machinespecific code on these machines for three algorithms: leastsquares linefitting, median finding, and a sparsematrix vector product. These results show
Distance Connectivity in Graphs and Digraphs
"... Let G = (V, A) be a digraph with diameter D � = 1. For a given integer 2 ≤ t ≤ D, the tdistance connectivity κ(t) of G is the minimum cardinality of an x → y separating set over all the pairs of vertices x, y which are at distance d(x, y) ≥ t. The tdistance edge connectivity λ(t) of G is defined ..."
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arbitrary integers c2 ≤... ≤ cD, D> 3, as the values of its tdistance connectivities κ(2) = c2,..., κ(D) = cD. Besides, a digraph that shows the independence of the parameters κ(t), λ(t), and δ(t) is constructed. Also we derive some results on the distance connectivities of digraphs, as well
Graph with extremal connectivity index
 Novi Sad J. Math
"... Abstract. Let G be a graph and δv the degree of its vertex v. The connectivity index of G is χ = � (δu δv) −1/2, with the summation ranging over all pairs of adjacent vertices of G. We offer a simple proof that (a) among nvertex graphs without isolated vertices, the star has minimal χvalue, and (b ..."
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Cited by 4 (0 self)
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Abstract. Let G be a graph and δv the degree of its vertex v. The connectivity index of G is χ = � (δu δv) −1/2, with the summation ranging over all pairs of adjacent vertices of G. We offer a simple proof that (a) among nvertex graphs without isolated vertices, the star has minimal χvalue
The connectivity of addition Cayley graphs
 Electronic Notes in Discrete Mathematics 29
, 2007
"... Abstract. For any finite abelian group G and any subset S ⊆ G, we determine the connectivity of the addition Cayley graph induced by S on G. Moreover, we show that if this graph is not complete, then it possesses a minimum vertex cut of a special, explicitly described form. 1. Background: addition C ..."
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Cited by 4 (1 self)
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Abstract. For any finite abelian group G and any subset S ⊆ G, we determine the connectivity of the addition Cayley graph induced by S on G. Moreover, we show that if this graph is not complete, then it possesses a minimum vertex cut of a special, explicitly described form. 1. Background: addition
HIGHER CONNECTIVITY OF GRAPH COLORING COMPLEXES
, 2005
"... The main result of this paper is a proof of the following conjecture of Babson & Kozlov: Theorem. Let G be a graph of maximal valency d, then the complex Hom (G, Kn) is at least (n − d − 2)connected. Here Hom (−, −) denotes the polyhedral complex introduced by Lovász to study the topological l ..."
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Cited by 13 (0 self)
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lower bounds for chromatic numbers of graphs. We will also prove, as a corollary to the main theorem, that the complex Hom (C2r+1, Kn) is (n − 4)connected, for n ≥ 3.
Results 1  10
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981