We are given a graph G(V,E) .

How to calculate the number of vertices and edges for L(G)(line-graph of G) , L(L(G)) and L(L(L(G))) without actually constructing them.

For, L(G) , the number of vertices in L(G) is equivalent to number of edges in G ,each vertex of degree k in the original graph G creates k(k−1)/2 edges in the line graph .

Reference : https://mathworld.wolfram.com/Claw-FreeGraph.html

https://mathworld.wolfram.com/LineGraph.html

But how to do calculations of the same for L(L(G)) and L(L(L(G))) without actually constructing them.