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Computing, 1978
According to the classification of labelled graph grammars by Nagl [4], it can be shown that the class of context-sensitive graph languages is equivalent to the class of context-free graph languages and the context-free graph languages properly include the regular graph languages.
Leon S. Levy, Kang Yueh
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According to the classification of labelled graph grammars by Nagl [4], it can be shown that the class of context-sensitive graph languages is equivalent to the class of context-free graph languages and the context-free graph languages properly include the regular graph languages.
Leon S. Levy, Kang Yueh
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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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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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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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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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Graph antimagic labeling: A survey
Discrete Mathematics, Algorithms and Applications, 2023An antimagic labeling of a simple graph [Formula: see text] is a bijection [Formula: see text] such that [Formula: see text] for any two vertices [Formula: see text] in [Formula: see text]. We survey the results about antimagic labelings and other labelings motivated by antimagic labelings of graphs, and present some conjectures and open questions.
Jingxiang Jin, Zhuojie Tu
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On sequential labelings of graphs
Journal of Graph Theory, 1983AbstractA valuation on a simple graph G is an assignment of labels to the vertices of G which induces an assignment of labels to the edges of G. β‐valuations, also called graceful labelings, and α‐valuations, a subclass of graceful labelings, have an extensive literature; harmonious labelings have been introduced recently by Graham and Sloane.
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Antimagic Labelings of Join Graphs
Mathematics in Computer Science, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martin Baca +3 more
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ODD GRACEFUL LABELINGS OF GRAPHS
Discrete Mathematics, Algorithms and Applications, 2009A graph G = (V(G), E(G)) with q edges is said to be odd graceful if there exists an injection f from V(G) to {0, 1, 2, …, 2q - 1} such that the edge labeling set is {1, 3, 5, …, 2q - 1} with each edge xy assigned the label |f(x) - f(y)|. In this paper, we prove that Pn × Pm (m = 2, 3, 4), generalized crown graphs Cn ⊙ K1,t and gear graphs are odd ...
Zhen-Bin Gao +2 more
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Enantiomeric Labeling of Reaction Graphs
Journal of Chemical Information and Computer Sciences, 1998We examine systematically the possibility that a given reaction graph connects enantiomers. We define an enantiomeric labeling as a way to dispose enantiomers on the graph according to specified conditions. Since reaction graphs have to be symmetric, we have derived the set of enantiomeric labelings for every symmetric graph having less than 20 ...
Brocas, Jean +2 more
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