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Group connectivity of certain graphs
 Ars Combin
, 2008
"... Let G be an undirected graph, A be an (additive) Abelian group and A ∗ = A − {0}. A graph G is Aconnected if G has an orientation such that for every function b: V (G) ↦ → A satisfying ∑ v∈V (G) b(v) = 0, there is a function f: E(G) ↦ → A ∗ such that at each vertex v ∈ V (G), the net flow out of ..."
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Cited by 6 (2 self)
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Let G be an undirected graph, A be an (additive) Abelian group and A ∗ = A − {0}. A graph G is Aconnected if G has an orientation such that for every function b: V (G) ↦ → A satisfying ∑ v∈V (G) b(v) = 0, there is a function f: E(G) ↦ → A ∗ such that at each vertex v ∈ V (G), the net flow out
On the Construction of Certain Graphs
, 1966
"... Denote by G(n) a graph of n vertices and by G(n; m) a graph of n vertices and in edges. I(G) denotes the cardinal number of the largest independent set of vertices (i.e., the largest set x il,..., xr,, r = I(G) of vertices of G no two of which are joined by an edge). v(x), the valency of the vertex ..."
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Denote by G(n) a graph of n vertices and by G(n; m) a graph of n vertices and in edges. I(G) denotes the cardinal number of the largest independent set of vertices (i.e., the largest set x il,..., xr,, r = I(G) of vertices of G no two of which are joined by an edge). v(x), the valency of the vertex
On Spanning Trees of Certain Graphs
"... Many classes of graphs have simple and elegant formulas for counting the number of spanning trees contained in them, but few have equally simple proofs. Here we present several such classes and oer two methods of attack. 1 ..."
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Many classes of graphs have simple and elegant formulas for counting the number of spanning trees contained in them, but few have equally simple proofs. Here we present several such classes and oer two methods of attack. 1
TColoring on Certain Graphs
"... Given a graph ܩ = (ܸ,ܧ) and a set T of nonnegative integers containing 0, a Tcoloring of G is an integer function ݂ of the vertices of G such that ݂(ݑ) − ݂(ݒ)  ∉ ܶ whenever ݑ ݒ ∈ ܧ. The ..."
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Given a graph ܩ = (ܸ,ܧ) and a set T of nonnegative integers containing 0, a Tcoloring of G is an integer function ݂ of the vertices of G such that ݂(ݑ) − ݂(ݒ)  ∉ ܶ whenever ݑ ݒ ∈ ܧ. The
On complete topological subgraphs of certain graphs
 Annales Univ. Sci. Budapest
, 1969
"... Let G he a graph. We say that G contains a complete kgon if there are!c vertices of G any two of which are connected by an edge, we say that it contains a complete topological kgon if it contains k vertices any two of which are connected by paths no two of which have a common vertex (except endpoi ..."
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Cited by 3 (0 self)
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Let G he a graph. We say that G contains a complete kgon if there are!c vertices of G any two of which are connected by an edge, we say that it contains a complete topological kgon if it contains k vertices any two of which are connected by paths no two of which have a common vertex (except
Product irregularity strength of certain graphs
, 2013
"... Consider a simple graph G with no isolated edges and at most one isolated vertex. A labeling w: E(G) → {1, 2,...,m} is called product irregular, if all product degrees pdG(v) = e3v w(e) are distinct. The goal is to obtain a product irregular labeling that minimizes the maximal label. This minimal ..."
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Consider a simple graph G with no isolated edges and at most one isolated vertex. A labeling w: E(G) → {1, 2,...,m} is called product irregular, if all product degrees pdG(v) = e3v w(e) are distinct. The goal is to obtain a product irregular labeling that minimizes the maximal label
Optimal tristance anticodes in certain graphs
 J. Combin. Theory Ser. A
, 2006
"... For z1, z2, z3 ∈ Z n, the tristance d3(z1, z2, z3) is a generalization of the L1distance on Z n to a quantity that reflects the relative dispersion of three points rather than two. A tristance anticode Ad of diameter d is a subset of Z n with the property that d3(z1, z2, z3) � d for all z1, z2, z3 ..."
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Cited by 3 (1 self)
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For z1, z2, z3 ∈ Z n, the tristance d3(z1, z2, z3) is a generalization of the L1distance on Z n to a quantity that reflects the relative dispersion of three points rather than two. A tristance anticode Ad of diameter d is a subset of Z n with the property that d3(z1, z2, z3) � d for all z1, z2, z3 ∈ Ad. An anticode is optimal if it has the largest possible cardinality for its diameter d. We determine the cardinality and completely classify the optimal tristance anticodes in Z 2 for all diameters d � 1. We then generalize this result to two related distance models: a different distance structure on Z 2 where d(z1, z2) = 1 if z1, z2 are adjacent either horizontally, vertically, or diagonally, and the distance structure obtained when Z 2 is replaced by the hexagonal lattice A2. We also investigate optimal tristance anticodes in Z 3 and optimal quadristance anticodes in Z 2, and provide bounds on their cardinality. We conclude with a brief discussion of the applications of our results to multidimensional interleaving schemes and to connectivity loci in the game of Go.
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Results 1  10
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