The neighbourhood polynomial of certain networks

Abstract

For connected graph G, the neighbourhood polynomial is defined as N(G, x) = ∑UϵN(G )x|U| ([4]) where (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 neighbor. Recently, Husin and Hasni (2018) [8] compute the neighbourhood polynomial for some families of dendrimers. In this paper, we examine neighbourhood polynomial of some interested standard graph networks like silicate, hexagonal and oxide networks.

Topics & Concepts