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The combinatorial heat and wave equations on all finite Cayley and cosetgraphs with discrete time variable was solved by Lal {\it et al}. In thispaper, the results of the above paper are extended for infinite Cayley andcoset graphs, whenever the associated groups are discrete, abelian and finitelygenerated. Furthermore, we study the solution of the combinatorial heat andwave equations on a $k$-regular tree whose associated group is a non-abelianfree group on $k$ generators, each of order~$2$. It turns out that in case ofCayley graphs the solutions to combinatorial heat and wave equations areweighted sum of the initial functions over balls of certain radius which aredependent on the discrete time variable.

Combinatorial Heat and Wave Equations on Certain Classes of Infinite Cayley and Coset Graphs