The Neighbourhood Polynomial of some Nanostructures

The neighbourhood polynomial g , is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph. in other word n(g,x)=∑u∈n(g)^ x^|u|, where n(g) is neighbourhood complex of a graph, whose vertices are the vertices of the graph and faces are subsets of vertices that have a common neighbour. in this paper we compute this polynomial for some nanostructures.