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Another extremal problem for Turan graphs. (English) Zbl 0629.05041
Let K(G) and $$\omega$$ (G) be the clique graph and clique number of a graph G. For $$1<r<n$$, let $$F(n,r)=\max_{G}\{| K(G)|:| V(G)| =n$$ and $$\omega (G)=r\}$$. A Turan graph $$T(n,r)$$ is a multipartite graph with vertices $$v_ 1,v_ 2,...,v_ n$$, and $$v_ iv_ j\in E(G)$$ if and only if $$i\neq j$$ (mod r). Theorem: Let G be a graph of order n with $$\omega (G)=r<n$$. Then $$| K(G)| =F(n,r)$$ if and only if $$G\sim T(n,r)$$.
Reviewer: S.F.Kapoor

##### MSC:
 05C35 Extremal problems in graph theory
##### Keywords:
clique graph; clique number; Turan graph; multipartite graph
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##### References:
 [1] BollobĂˇs, B, Extremal graph theory, (1978), Academic Press London · Zbl 0419.05031 [2] Hedman, B, The maximum number of cliques in dense graphs, Discrete math., 54, 161-166, (1985) · Zbl 0569.05029 [3] Moon, J.W; Moser, L, On cliques in graphs, Israel J. math., 3, 23-28, (1965) · Zbl 0144.23205 [4] Roman, S, The maximum number of q-cliques in a graph with no p-clique, Discrete math., 14, 365-371, (1976) · Zbl 0319.05126 [5] Turan, P, On an extremal problem in graph theory, Mat. fiz. lapok, 48, 436-452, (1941)
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