In a recent paper , Hamelink obtains an interesting sufficient condition for a graph to be a clique graph. In this paper, we give related conditions which are necessary as well as sufficient. As an application of our result we show that Hamelink's condition is also necessary in certain special cases and that here it can be greatly simplified. As another application, we derive certain theorems useful in practice in reducing the question of whether a given graph is a clique graph to whether certain smaller or simpler graphs are.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics