Results 21 to 30 of about 1,327,272 (305)
Bounds for Distinguishing Invariants of Infinite Graphs [PDF]
Electronic Journal of Combinatorics, 2017 We consider infinite graphs. The distinguishing number $D(G)$ of a graph $G$ is the minimum number of colours in a vertex colouring of $G$ that is preserved only by the trivial automorphism.
W. Imrich +3 more
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Graphs whose vertex set can be partitioned into a total dominating set and an independent dominating set [PDF]
Opuscula MathematicaA graph \(G\) whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. We give constructions that yield infinite families of graphs that are TI-graphs, as well as constructions that yield ...
Teresa W. Haynes, Michael A. Henning
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Distinguishing infinite graphs with bounded degrees [PDF]
Journal of Graph Theory, 2018 Call a colouring of a graph distinguishing if the only colour preserving automorphism is the identity. A conjecture of Tucker states that if every automorphism of a connected graph G $G$ moves infinitely many vertices, then there is a distinguishing 2 ...
Florian Lehner +2 more
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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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Seidel Integral Complete Split Graphs [PDF]
Mathematics Interdisciplinary Research, 2019 In the paper we consider a generalized join operation, that is, the H-join on graphs where H is an arbitrary graph. In terms of Seidel matrix of graphs we determine the Seidel spectrum of the graphs obtained by this operation on regular graphs.
Pavel Hic +2 more
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Norms, kernels and eigenvalues of some infinite graphs [PDF]
Operators and Matrices, 2018 In these paper we study the adjacency matrix of some infinite graphs, which we call the shift operator on the $L^p$ space of the graph. In particular, we establish norm estimates, we find the norm for some cases, we decide the triviality of the kernel of
Aahan Agrawal +4 more
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An Automaton Learning Approach to Solving Safety Games over Infinite Graphs [PDF]
International Conference on Tools and Algorithms for Construction and Analysis of Systems, 2016 We propose a method to construct finite-state reactive controllers for systems whose interactions with their adversarial environment are modeled by infinite-duration two-player games over possibly infinite graphs.
D. Neider, U. Topcu
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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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Controllability of localised quantum states on infinite graphs through bilinear control fields [PDF]
International Journal of Control, 2018 In this work, we consider the bilinear Schrödinger equation (BSE) in the Hilbert space with an infinite graph. The Laplacian is equipped with self-adjoint boundary conditions, B is a bounded symmetric operator and with T>0. We study the well-posedness of
K. Ammari, Alessandro Duca
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