The PI and Edge Szeged Indices of Carbon Nanocones CNC3[n] and CNC4[n]

The Padmakar–Ivan (PI) index of a graph G is defined as PI(G) = Σ[mu(e)+ mv(e)], where mu(e) is the number of edges of G lying closer to u than to v, mv(e) is the number of edges of G lying closer to v than to u and summation goes over all edges of G. The edge Szeged index is a new molecular structure descriptor equal to the sum of products mu(e)mv(e) over all edges e = uv of the molecular graph G, where mu(e) is the number of edges whose distance to vertex u is smaller than the distance to vertex v, and mv(e) is defined analogously. In this paper, the PI and edge Szeged indices of one–heptagonal carbon nanocone CNC7[n] is computed for the first time.