Results 231 to 240 of about 24,189 (265)
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On Partitional Labelings of Graphs
Mathematics in Computer Science, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Rikio Ichishima, Akito Oshima
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SIAM Journal on Discrete Mathematics, 1992
Summary: Given a graph \(G\) and positive integer \(d\), the pair-labeling number \(r^*(G,d)\) is the minimum \(n\) such that each vertex in \(G\) can be assigned a pair of numbers from \(\{0,1,\dots,n-1\}\) so that any two numbers used at adjacent vertices differ by at least \(d\) modulo \(n\).
David R. Guichard, John W. Krussel
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Summary: Given a graph \(G\) and positive integer \(d\), the pair-labeling number \(r^*(G,d)\) is the minimum \(n\) such that each vertex in \(G\) can be assigned a pair of numbers from \(\{0,1,\dots,n-1\}\) so that any two numbers used at adjacent vertices differ by at least \(d\) modulo \(n\).
David R. Guichard, John W. Krussel
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Graphs and Combinatorics, 1997
A mapping \(f: E\to\{0,1\}^m\) of a graph \(G=(V,E)\) is called a mod 2 coding of \(G\), if the induced mapping \(g:V\to \{0,1\}^m\), defined by \(g(v)= \sum_{u\in V,\{u,v\}\in E}f(\{u,v\})\) assigns a different number to each vertex, where summations are taken modulo 2.
Louis Caccetta, Rui-Zhong Jia
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A mapping \(f: E\to\{0,1\}^m\) of a graph \(G=(V,E)\) is called a mod 2 coding of \(G\), if the induced mapping \(g:V\to \{0,1\}^m\), defined by \(g(v)= \sum_{u\in V,\{u,v\}\in E}f(\{u,v\})\) assigns a different number to each vertex, where summations are taken modulo 2.
Louis Caccetta, Rui-Zhong Jia
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2018 IEEE 34th International Conference on Data Engineering (ICDE), 2018
Nowadays, a graph serves as a fundamental data structure for many applications. As graph edges stream in, users are often only interested in the recent data. In data exploration, how to store and process such massive amounts of graph stream data becomes a significant problem.
Chunyao Song, Tingjian Ge
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Nowadays, a graph serves as a fundamental data structure for many applications. As graph edges stream in, users are often only interested in the recent data. In data exploration, how to store and process such massive amounts of graph stream data becomes a significant problem.
Chunyao Song, Tingjian Ge
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Journal of Graph Theory, 1979
AbstractGiven a graph Γ an abelian group G, and a labeling of the vertices of Γ with elements of G, necessary and sufficient conditions are stated for the existence of a labeling of the edges in which the label of each vertex equals the product of the labels of its incident edges. Such an edge labeling is called compatible.
Paul H. Edelman, Michael E. Saks
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AbstractGiven a graph Γ an abelian group G, and a labeling of the vertices of Γ with elements of G, necessary and sufficient conditions are stated for the existence of a labeling of the edges in which the label of each vertex equals the product of the labels of its incident edges. Such an edge labeling is called compatible.
Paul H. Edelman, Michael E. Saks
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Discrete Mathematics, Algorithms and Applications, 2019
The notion of maximal labeling, optimal maximal labeling and the maximal index of a graph using the nonunit elements of a commutative ring with identity are introduced and studied. The maximal index of complete graphs, complete bipartite graphs are given. Maximal index of cycles of order up to [Formula: see text] and Petersen graph are also given.
Arti Sharma, Atul Gaur
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The notion of maximal labeling, optimal maximal labeling and the maximal index of a graph using the nonunit elements of a commutative ring with identity are introduced and studied. The maximal index of complete graphs, complete bipartite graphs are given. Maximal index of cycles of order up to [Formula: see text] and Petersen graph are also given.
Arti Sharma, Atul Gaur
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Graphs and Combinatorics, 1998
Let \(G=(V,E)\) be a graph which is not a tree. For an injective function \(g:V\to\{0,\dots,| E| -1\}\) define \(g^*:E\to{\mathbb{N}}\) such that \(g^*(uv)=g(u)+g(v)\) for all edges \(uv\in E\). The graph \(G\) is called sequential if \(g^*(E)\) is a sequence of distinct consecutive integers. Furthermore, for graphs \(G\) and \(H\) denote by \(G\odot H\
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Let \(G=(V,E)\) be a graph which is not a tree. For an injective function \(g:V\to\{0,\dots,| E| -1\}\) define \(g^*:E\to{\mathbb{N}}\) such that \(g^*(uv)=g(u)+g(v)\) for all edges \(uv\in E\). The graph \(G\) is called sequential if \(g^*(E)\) is a sequence of distinct consecutive integers. Furthermore, for graphs \(G\) and \(H\) denote by \(G\odot H\
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Proceedings of the fifteenth annual ACM symposium on Theory of computing - STOC '83, 1983
We announce an algebraic approach to the problem of assigning canonical forms to graphs. We compute canonical forms and the associated canonical labelings (or renumberings) in polynomial time for graphs of bounded valence, in moderately exponential, exp(n½ + o(1)),time for general graphs, in subexponential, nlog n, time for tournaments and for 2-(n,k,l)
László Babai, Eugene M. Luks
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We announce an algebraic approach to the problem of assigning canonical forms to graphs. We compute canonical forms and the associated canonical labelings (or renumberings) in polynomial time for graphs of bounded valence, in moderately exponential, exp(n½ + o(1)),time for general graphs, in subexponential, nlog n, time for tournaments and for 2-(n,k,l)
László Babai, Eugene M. Luks
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Ars Comb., 1999
The authors investigate such integer labelings \(w\) (called ``magic'') of edges of a graph \(G\), in which \(\sum_{v\in e}w(e)\) is a constant \(s\) independent of the vertex \(v\). They introduce basis graphs of type I and II. For the type I a unique, up to a constant factor, labeling exists with \(s>0\) and no \(0\) label.
Gobel, F., Hoede, C.
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The authors investigate such integer labelings \(w\) (called ``magic'') of edges of a graph \(G\), in which \(\sum_{v\in e}w(e)\) is a constant \(s\) independent of the vertex \(v\). They introduce basis graphs of type I and II. For the type I a unique, up to a constant factor, labeling exists with \(s>0\) and no \(0\) label.
Gobel, F., Hoede, C.
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