Results 31 to 40 of about 1,555,658 (364)
Directed Polymers on Infinite Graphs [PDF]
Communications in Mathematical Physics, 2021 We study the directed polymer model for general graphs (beyond $\mathbb Z^d$) and random walks. We provide sufficient conditions for the existence or non-existence of a weak disorder phase, of an $L^2$ region, and of very strong disorder, in terms of properties of the graph and of the random walk. We study in some detail (biased) random walk on various
Clément Cosco +2 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
doaj +1 more source
On Hamilton decompositions of infinite circulant graphs [PDF]
, 2017 The natural infinite analogue of a (finite) Hamilton cycle is a two-way-infinite Hamilton path (connected spanning 2-valent subgraph). Although it is known that every connected 2k-valent infinite circulant graph has a two-way-infinite Hamilton path ...
Bryant, Darryn +3 more
core +2 more sources
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
semanticscholar +1 more source
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
semanticscholar +1 more source
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
doaj +1 more source
Schreier graphs of the Basilica group [PDF]
, 2010 With any self-similar action of a finitely generated group $G$ of automorphisms of a regular rooted tree $T$ can be naturally associated an infinite sequence of finite graphs $\{\Gamma_n\}_{n\geq 1}$, where $\Gamma_n$ is the Schreier graph of the action ...
D'Angeli, Daniele +3 more
core +5 more sources
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
semanticscholar +1 more source
The center of an infinite graph
Discrete Mathematics, 1996 In this note we extend the notion of the center of a graph to infinite graphs. Thus, a vertex is in the center of the infinite graph G if it is in the center of an increasing family of finite subgraphs covering G. We give different characterizations of when a vertex is in the center of an infinite graph and we prove that any infinite graph with at ...
Boza Prieto, Luis +2 more
openaire +4 more sources
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
doaj +1 more source