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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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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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Universal Communication, Universal Graphs, and Graph Labeling
Information Technology Convergence and Services, 2019We introduce a communication model called universal SMP, in which Alice and Bob receive a function $f$ belonging to a family $\mathcal{F}$, and inputs $x$ and $y$.
Nathaniel Harms
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Multiplex Labeling Graph for Near-Online Tracking in Crowded Scenes
IEEE Internet of Things Journal, 2020In recent years, the demand for intelligent devices related to the Internet of Things (IoT) is rapidly increasing. In the field of computer vision, many algorithms have been preinstalled in IoT devices to achieve higher efficiency, such as face ...
Yang Zhang +5 more
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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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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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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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On the properties of anti fuzzy graph magic labeling
THE 2ND INTERNATIONAL CONFERENCE ON SCIENCE, MATHEMATICS, ENVIRONMENT, AND EDUCATION, 2019Graph labeling is one of the famous topics in the study of fuzzy graph. This article was considering to anti fuzzy graph magic labeling. As a new concept in anti fuzzy graph, we adapted from the previous study of fuzzy graph about the related concept ...
Adika Setia Brata +4 more
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On the properties of bipolar anti fuzzy graph magic labeling
THE 2ND INTERNATIONAL CONFERENCE ON SCIENCE, MATHEMATICS, ENVIRONMENT, AND EDUCATION, 2019This article was considering to bipolar anti fuzzy graph magic labeling. Bipolar anti fuzzy graph be seen as new concept, therefore to find the properties, we adapted from the previous study of bipolar fuzzy graph.
Ilman Firmansa +5 more
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