Chromatic Polynomials Of Some (m,l)-Hyperwheels

In this paper, using a standard method of computing the chromatic polynomial of hypergraphs, we introduce a new reduction theorem which allows us to find explicit formulae for the chromatic polynomials of some (complete) non-uniform $(m,l)-$hyperwheels and non-uniform $(m,l)-$hyperfans. These hypergraphs, constructed through a ``join" graph operation, are some generalizations of the well-known wheel and fan graphs, respectively. Further, we revisit some results concerning these graphs and present their chromatic polynomials in a standard form that involves the Stirling numbers of the second kind.