Busemann points of infinite graphs
WebBusemann Points of Infinite Graphs Webster, Corran ; Winchester, Adam We provide a geometric condition which determines whether or not every point on the metric boundary … WebJun 8, 2016 · We find out that the order 17 is the smallest case providing two non-isomorphic 4-regular circulant graphs with the same Wiener index. Some open problems and questions are listed. No full-text...
Busemann points of infinite graphs
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WebDec 29, 2006 · Lemmens and Walsh show that there is a metric on the set of Busemann points of a Hilbert geometry called the detour metric which is possibly infinite. ... Isometries of the Hilbert Metric... WebEvery ray c determines a Busemann function B e : R 2 -+ R which can be interpreted as the distance function from the "point at infinity" determined by c. Busemann [5] calls a ray E …
WebOct 17, 2003 · Busemann Points of Infinite Graphs DOI: arXiv Authors: Corran Webster Adam Winchester Request full-text Abstract We provide a geometric condition which … WebApr 11, 2006 · BUSEMANN POINTS OF INFINITE GRAPHS CORRAN STER AND ADAM WINCHESTER Abstract. We provide a geometric condition which determines …
WebWe provide a geometric condition which determines whether or not every point on the metric boundary of a graph with the standard path metric is a Busemann point, that is it is the limit point of a geodesic ray. We apply this and a related condition to investigate the structure of the metric boundary of Cayley graphs. WebBUSEMANN POINTS OF INFINITE GRAPHS CORRAN STER AND ADAM WINCHESTER Abstract. We provide a geometric condition which determines …
Webmeasure on the set of words indexing the graphs, for almost all the infinite graphs, the boundary consists of four Busemann points and countably many non-Busemann points. View Show...
WebTake one ray [0, ∞] 0 \left[0,\infty\right] [ 0 , ∞ ] that will be geodsic, then add an infinite number of points at distance 1 1 1 1 to the point 0 and distance 2 2 2 2 to each other. Then at each point n 𝑛 n italic_n on the ray, connect it to one of the points around 0 with a geodesic segment of length n − 1 / 2 𝑛 1 2 n-1/2 italic ... eventcomWebEnds of graphs may be used (via Cayley graphs) to define ends of finitely generated groups. Finitely generated infinite groups have one, two, or infinitely many ends, and the … first hawaiian insuranceWebIn particular, we are able to classify Busemann and non-Busemann points of the metric boundary. It turns out that, with respect to the uniform Bernoulli measure on the set of words indexing the graphs, for almost all the infinite graphs, the boundary consists of four Busemann points and countably many non-Busemann points. first hawaiian insurance company