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9,892
The formalization of simple graphs
 Journal of Formalized Mathematics
, 1994
"... Summary. A graph is simple when • it is nondirected, • there is at most one edge between two vertices, • there is no loop of length one. A formalization of simple graphs is given from scratch. There is already an article [10], dealing with the similar subject. It is not used as a startingpoint, be ..."
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Cited by 21 (0 self)
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Summary. A graph is simple when • it is nondirected, • there is at most one edge between two vertices, • there is no loop of length one. A formalization of simple graphs is given from scratch. There is already an article [10], dealing with the similar subject. It is not used as a starting
On Equational Simple Graphs
, 1997
"... We consider simple graphs that can be obtained from the infinite complete binary tree B by some simple languagetheoretic operations. Their decision problems for sentences in monadic secondorder logic are reduced to those of B in a straightforward manner and therefore are solvable by the famous res ..."
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Cited by 13 (1 self)
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We consider simple graphs that can be obtained from the infinite complete binary tree B by some simple languagetheoretic operations. Their decision problems for sentences in monadic secondorder logic are reduced to those of B in a straightforward manner and therefore are solvable by the famous
An index formula for simple graphs
, 2012
"... Abstract. We prove that any odd dimensional geometric graph G = (V, E) has zero curvature everywhere. To do so, we prove that for every injective function f on the vertex set V of a simple graph the index formula 1 [1 − 2 χ(S(x))/2 − χ(Bf (x))] = (if (x) + i−f (x))/2 = jf (x) holds, where if (x) is ..."
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Cited by 7 (7 self)
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Abstract. We prove that any odd dimensional geometric graph G = (V, E) has zero curvature everywhere. To do so, we prove that for every injective function f on the vertex set V of a simple graph the index formula 1 [1 − 2 χ(S(x))/2 − χ(Bf (x))] = (if (x) + i−f (x))/2 = jf (x) holds, where if (x
Editing simple graphs
 J. Graph Algorithms Appl
"... Abstract We study the complexity of turning a given graph, by edge editing, into a target graph whose criticalclique graph is any fixed graph. The problem came up in practice, in an effort of mining huge word similarity graphs for well structured word clusters. It also adds to the rich field of gr ..."
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Cited by 2 (0 self)
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Abstract We study the complexity of turning a given graph, by edge editing, into a target graph whose criticalclique graph is any fixed graph. The problem came up in practice, in an effort of mining huge word similarity graphs for well structured word clusters. It also adds to the rich field
Simple Graph Editing
"... Applications of mathematics occasionally produce models that are best understood and visualized as directed or undirected graphs. Computer aids to mathematicians can contribute to the understanding and communication of this information, especially if wellintegrated into the problemsolving working ..."
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Applications of mathematics occasionally produce models that are best understood and visualized as directed or undirected graphs. Computer aids to mathematicians can contribute to the understanding and communication of this information, especially if wellintegrated into the problemsolving working
On fcolorings of simple graphs
"... Let G be a graph and let f be a function which assigns a positive integer f(v) to each vertex v ∈ V (G). An fcoloring of G is an edgecoloring such that ..."
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Let G be a graph and let f be a function which assigns a positive integer f(v) to each vertex v ∈ V (G). An fcoloring of G is an edgecoloring such that
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 1791 (69 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
Supermagic Coverings of Some Simple Graphs
"... Abstract: A simple graph G = (V,E) admits an Hcovering if every edge in E belongs to a subgraph of G isomorphic to H. We say that G is Smarandachely pair {s, l} Hmagic if there is a total labeling f: V ∪ E → {1, 2, 3, · · · , V  + E} such that there are subgraphs H1 = (V1, E1) and H2 = (V2, ..."
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Abstract: A simple graph G = (V,E) admits an Hcovering if every edge in E belongs to a subgraph of G isomorphic to H. We say that G is Smarandachely pair {s, l} Hmagic if there is a total labeling f: V ∪ E → {1, 2, 3, · · · , V  + E} such that there are subgraphs H1 = (V1, E1) and H2 = (V2
The geometry of graphs and some of its algorithmic applications
 COMBINATORICA
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that res ..."
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Cited by 524 (19 self)
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their geometric images. In this paper we develop efficient algorithms for embedding graphs lowdimensionally with a small distortion. Further algorithmic applications include: 0 A simple, unified approach to a number of problems on multicommodity flows, including the LeightonRae Theorem [29] and some of its ex
Results 1  10
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9,892