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Convergence of sequences of iterated triangular line graphs

✍ Scribed by David Dorrough

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
333 KB
Volume
161
Category
Article
ISSN
0012-365X

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✦ Synopsis

The triangular line graph T(G) of a graph G is the graph with vertex set E(G), with two distinct vertices e and f of T(G) adjacent if and only if the edges e and f belong to a common copy ofK 3 in G. For n/> 1, the nth iterated triangular line graph T"(G) of a graph G is defined as T(T n-I(G)), where TΒ°(G) = G. In I-4] it is shown that the sequence of iterated triangular line graphs of a graph G converges to r disjoint copies of K 3, for some r/> 0. Here we determine how many iterations are required for convergence, and how many disjoint copies of K 3 are obtained.

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