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IOP PUBLISHING LTD
DOI: 10.1088/1742-6596/1008/1/012028
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The neighbourhood polynomial N(G, x) is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph and it is defined as (G, x) = Sigma(U is an element of N(G)) x(vertical bar U vertical bar), where N(G) is neighbourhood complex of a graph, whose vertices of the graph and faces are subsets of vertices that have a common neighbour. A dendrimers is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, we compute this polynomial for some families of dendrimer.
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