Answer to Question #125350 in General Chemistry for Zahra Ghorbani

Question

Please,guide me to calculate PI for different fullerenes.

Answer 1

What is a fullerene? It is a carbon allotrope and its molecule is made up of carbon atoms attached together by single and double bonds to form either a partially or closed mesh or a cage with many carbon atom.

Simple and finite graphs are used.

Let G represent the graph, V(G) represents vertex sets and E(G) the edge sets.Vertex sets are the atoms and the edges are chemical bonds for a molecular graph.G is a simple molecular graph with n-vertex , e=uv be an edge and d(u,w) denotes the distance between u and w vertices.

m_u (e) denotes the number of edges lying near to the vertex u than vertex v.

m_v (e) is defined the same way.

$PI(G)=\Sigma^r_{i=1}=\lvert E_i \lvert (m_{ui}(e_i)+m_{vi}(e_i))\ where,\newline E_1,E_2.........,E_r\ with \ representatives \ e_1,e_2....e_r\ where\ e_i=u_iv_i$

To evaluate the PI index, we make some three assumptions.

1. When n is odd
2. When n is even two cases are considered that n is divisible by 4 or assume that n is an even positive number that is divisible by 4.