The Neighbourhood Polynomial of some Nanostructures

Document Type: Research Paper


Yazd University


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 $N(G,x)=sum_{Uin N(G)} x^{|U|}$, 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.


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