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Showing 1 to 18 of 18 for “"Cayley Graphs"”.
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Automata on Cayley Graphs
… two properties of a tape must, in fact, be the Cayley graph of a suitable group. Recent investigations by various authors have begun to shed some light on what promises to be intimate connections between the geometry of a Cayley graph and the group-theoretic properties of the underlying group.
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Universality of Cutoff for Random Walks on Random Cayley Graphs
Consider the random Cayley graph of a finite group G with respect to k generators chosen uniformly at random. This draws a Cayley graph uniformly amongst all degree-k Cayley graphs of G. A conjecture of Aldous and Diaconis (1985) from the '80s asserts, for k ≫ log |G|, the following: • the random …
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Diameter, Girth And Other Properties Of Highly Symmetric Graphs
… with the unifying theme being the properties of graphs which have a high degree of symmetry. In the degree-diameter problem, we consider the question of finding asymptotically large graphs of given degree and diameter. We improve a number of the current best published results in the case of …
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Achieving Fair Distribution with Choice
… over toroidal grids (and more generally, Cayley graphs on groups), integrating local information, bounded memory and choice at individual nodes. The research is motivated by recent work on deterministic random walks, and applications in multi-agent systems. Several results regarding …
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THE LOW-INTENSITY LIMIT OF BERNOULLI-VORONOI AND POISSON-VORONOI MEASURES
… this limit on d-regular trees and other infinite Cayley graphs. A related model in the continuous setting is the Poisson-Voronoi model, which can be defined on any metric space. In this setting, the nuclei of the Voronoi tiles are obtained by a Poisson process, with intensity lambda, and the …
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Problems in the Theory of Convergence Spaces
… spaces, representation of reflexive digraphs as convergence spaces, construction of differential calculi on convergence spaces, mereology on convergence spaces, and construction of a universal homogeneous pretopological space. First, we generalize Kolmogorov separation from topological …
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Applications of Schur rings in algebraic combinatorics: graphs, partial difference sets and cyclotomic schemes
… considered: (1) characterization of commuting graphs, (2) consideration of strongly regular graphs and partial difference sets and (3) investigation of cyclotomic schemes. The first part deals with graphs with commuting adjacency matrices. Here, we give results for commuting regular graphs and …
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Cayley maps for certain cyclic groups with odd generators
… work for both oral and written presentation; A Cayley graph provides us with a discrete model for a finite group with specified generating set. It is desirable to represent such structures in their simplest form and also so that certain symmetries are emphasized. By simplest form, we mean to …
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Computational and Statistical Detection of High-Dimensional Latent Space Structure in Random Networks
… Fourier coefficients of random geometric graphs based on a representation of spherical random geometric graphs as Erdős-Rényi with few planted edges. This part of the thesis is based on [BB24b]. Chapter 3: The conjectured optimality of the signed triangle count and the relavance of …
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Persistent patrolling in the presence of adversarial observers
… walks, Markov processes, and random walks on Cayley graphs to ultimately model the game equilibrium when the team of patrollers execute so-called "presence patrols." Police and military forces commonly execute this type of patrolling to project their presence across an environment in an effort …
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Group-invariant random processes
… point process on Rd and examine what types of graphs can be defined on the points of the process in such a way that the point process and the graph have an equivariant distribution. We show that 1-ended trees and Zn can be achieved for invariant point processes in Rd that satisfy some …
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Lines in Hales-Jewett cubes and other combinatorial results
… a generating set for the group, but in fact the Cayley graph of G with respect to these elements is highly connected, in the sense that it is an expander graph. Our proof of the Alon-Roichman Theorem gives an improvement to the known bounds. In Chapter 3, we study properties of random graphs …
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Symmetric Presentations and Generation
… based using MAGMA. We have also constructed Cayley graphs of the following groups, 2<sup>5</sup> : <em>S</em><sub>5</sub> over 2<sup><em>∗</em>5</sup> : <em>S</em><sub>5</sub>, <em>P</em><em>S</em><em>L</em>(2<em>, </em>8) over 2<sup><em>∗</em>7</sup> : <em>D</em><sub>14</sub>, …