Infinite Locally Random Graphs
نویسندگان
چکیده
Motivated by copying models of the web graph, Bonato and Janssen [3] introduced the following simple construction: given a graph G, for each vertex x and each subset X of its closed neighbourhood, add a new vertex y whose neighbours are exactly X. Iterating this construction yields a limit graph ↑G. Bonato and Janssen claimed that the limit graph is independent of G, and it is known as the infinite locally random graph. We show that this picture is incorrect: there are in fact infinitely many isomorphism classes of limit graph, and we give a classification. We also consider the inexhaustibility of these graphs.
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عنوان ژورنال:
- Internet Mathematics
دوره 3 شماره
صفحات -
تاریخ انتشار 2007