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.

Subject Classification:

• Primary 93A30
• Secondary 49K15

Keywords:

• Neighbourhood polynomial
• Hexagonal network
• Oxide networks
• Silicate networks