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Dismantlings and iterated clique graphs

✍ Scribed by M.E Frı́as-Armenta; V Neumann-Lara; M.A Pizaña

Book ID
108113414
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
190 KB
Volume
282
Category
Article
ISSN
0012-365X

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Iterated clique graphs with increasing d
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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

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If G is a graph, its clique graph, K(G), is the intersection graph of all its (maximal) cliques. Iterated clique graphs are then deÿned 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

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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^n−1^(__G__)) and __K__^1^(__G__) = __K__(__G__). Let the diameter diam(__G__) be the greatest distance between