Results 21 to 30 of about 17,750 (263)
Infinite families of asymmetric graphs
AKCE International Journal of Graphs and Combinatorics, 2020 A graph G is asymmetric if its automorphism group of vertices is trivial. Asymmetric graphs were introduced by Erdős and Rényi in 1963. They showed that the probability of a graph on n vertices being asymmetric tends to 1 as n tends to infinity.
Alejandra Brewer +5 more
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Linearly bounded infinite graphs [PDF]
Acta Informatica, 2005 Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs. These automata naturally accept the same languages as the linearly bounded machines defining them. We present some of
Carayol, Arnaud, Meyer, Antoine
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On the Metric Dimension of Infinite Graphs [PDF]
Electronic Notes in Discrete Mathematics, 2009 A set of vertices $S$ \emph{resolves} a graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of a graph $G$ is the minimum cardinality of a resolving set. In this paper we study the metric dimension of infinite graphs such that all its vertices have finite degree.
José Cáceres +4 more
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Characterising memory in infinite games [PDF]
Logical Methods in Computer ScienceThis paper is concerned with games of infinite duration played over potentially infinite graphs. Recently, Ohlmann (LICS 2022) presented a characterisation of objectives admitting optimal positional strategies, by means of universal graphs: an objective ...
Antonio Casares, Pierre Ohlmann
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On external presentations of infinite graphs [PDF]
Electronic Proceedings in Theoretical Computer Science, 2009 The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices.
Christophe Morvan
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On Transmission Irregular Cubic Graphs of an Arbitrary Order
Mathematics, 2022 The transmission of a vertex v of a graph G is the sum of distances from v to all the other vertices of G. A transmission irregular graph (TI graph) has mutually distinct vertex transmissions.
Anatoly Yu. Bezhaev, Andrey A. Dobrynin
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An introduction of F-graphs, a graph-theoretic representation of natural numbers
International Journal of Mathematics and Mathematical Sciences, 1992 A special type of family graphs (F-graphs, for brevity) are introduced. These are cactus-type graphs which form infinite families under an attachment operation. Some of the characterizing properties of F-graphs are discussed.
E. J. Farrell
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The Colouring Number of Infinite Graphs [PDF]
Combinatorica, 2019 We show that, given an infinite cardinal $μ$, a graph has colouring number at most $μ$ if and only if it contains neither of two types of subgraph. We also show that every graph with infinite colouring number has a well-ordering of its vertices that simultaneously witnesses its colouring number and its cardinality.
Nathan J. Bowler +3 more
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The Distinguishing Index of Infinite Graphs [PDF]
The Electronic Journal of Combinatorics, 2015 The distinguishing index $D^\prime(G)$ of a graph $G$ is the least cardinal $d$ such that $G$ has an edge colouring with $d$ colours that is only preserved by the trivial automorphism. This is similar to the notion of the distinguishing number $D(G)$ of a graph $G$, which is defined with respect to vertex colourings.We derive several bounds for ...
Broere, Izak, Pilsniak, Monika
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Discrete Mathematics, 2011 It has recently been shown that infinite matroids can be axiomatized in a way that is very similar to finite matroids and permits duality. This was previously thought impossible, since finitary infinite matroids must have non-finitary duals. In this paper we illustrate the new theory by exhibiting its implications for the cycle and bond matroids of ...
Henning Bruhn, Reinhard Diestel
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