Introducing Two Transformations in Fullerene Graphs, Star and Semi-Star

A perfect star packing in a given graph G can be defined as a spanning subgraph of G, wherein each component is isomorphic to the star graph K1,3. A perfect star packing of a fullerene graph G is of type P 0 if all the centers of stars lie on hexagons of G. Many fullerene graphs arise from smaller fullerene graphs by applying some transformations. In this paper, we introduce two transformations for fullerene graphs that have the perfect star packing of type P 0 and examine some characteristics of the graphs obtained from this transformation.‎.