# uniformly locally finite graph

A is a locally finite graph (http://planetmath.org/LocallyFiniteGraph) $(V,E)$ such that there exists an $M\in\mathbb{N}$ such that for every $x\in V$ we have that the degree of $x$, also denoted $\rho(x)$, is at most $M$. In other words there exists an $M\in\mathbb{N}$ such that for every $x\in V\,,\,\rho(x)\leq M$.

Note that the examples provided in locally finite graph (http://planetmath.org/LocallyFiniteGraph) are also examples of a uniformly locally finite graph since both graphs are regular (http://planetmath.org/RegularGraph) and have finite degree (http://planetmath.org/Degree7) at each vertex.

Title uniformly locally finite graph UniformlyLocallyFiniteGraph 2013-03-22 16:00:54 2013-03-22 16:00:54 sjm1979 (13837) sjm1979 (13837) 6 sjm1979 (13837) Definition msc 05C99 LocallyFiniteGraph