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Diameters of iterated clique graphs of chordal graphs

✍ Scribed by Bor-Liang Chen; Ko-Wei Lih

Publisher: John Wiley and Sons
Year: 1990
Tongue: English
Weight: 272 KB
Volume: 14
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190140311

No coin nor oath required. For personal study only.

✦ Synopsis

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 all pairs of vertices of G. We show that diam(K^n^(G)) = diam(G) — n if G is a connected chordal graph and n ≤ diam(G). This generalizes a similar result for time graphs by Bruce Hedman.

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