The difference between clique graphs and iterated clique graphs
β Scribed by Pablo De Caria
- Book ID
- 108120799
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 280 KB
- Volume
- 37
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
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## Abstract The clique graph __K__(__G__) of a graph is the intersection graph of maximal cliques of __G.__ The iterated clique graph __K__^__n__^(__G__) is inductively defined as __K__(K^nβ1^(__G__)) and __K__^1^(__G__) = __K__(__G__). Let the diameter diam(__G__) be the greatest distance between
A simple argument by Hedman shows that the diameter of a clique graph G differs by at most one from that of K(G), its clique graph. Hedman described examples of a graph G such that diam(K(G)) = diam(G) + 1 and asked in general about the existence of graphs such that diam(K i (G)) = diam(G) + i. Exam
If G is a graph, its clique graph, K(G), is the intersection graph of all its (maximal) cliques. Iterated clique graphs are then deΓΏned recursively by: K We study the relationship between distances in G and distances in K n (G). Then we apply these results to Johnson graphs to give a shorter and si