Edge-clique graphs

@article{Chartrand1991EdgecliqueG,
  title={Edge-clique graphs},
  author={Gary Chartrand and Sanjay Kapoor and Terry A. McKee and Farrokh Saba},
  journal={Graphs and Combinatorics},
  year={1991},
  volume={7},
  pages={253-264}
}
The edge-clique graph K(G) of a graph G is that graph whose vertices correspond to the edges of G and where two vertices of K(G) are adjacent whenever the corresponding edges of G belong to a common clique. It is shown that every edge-clique graph is a clique graph, and that if G is either an interval graph or a line graph, then so too is K(G). An algorithm… CONTINUE READING