A Nim game played on graphs II

Abstract

We consider a Nim game played on graphs, which was proposed and was named Nim on graphs in [4], and investigate its Grundy number using matchings of graphs. Especially, by virtue of this investigation, we can find the Grundy number of Nim on trees completely. Another result is that the problem of finding the Grundy number of Nim on cycles is resolved into that of Nim on trees. Thus, we find also the Grundy number of Nim on cycles completely.