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A result on iterated clique graphs

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

Lim Chong-Keang
Lim Chong-Keang
Affiliation:
Department of Mathematics, University of Malaya, Kuala Lumpur, Malaysia
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Abstract

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S. T. Hedetniemi and P. J. Slater have shown that if G is a triangle-free connected graph with at least three vertices, then

where K(G) is the clique graph of G and K2(G) = K(K(G)) is the first iterated clique graph. In this paper, we generalize the above result to a wider class of graphs.

MSC classification

Secondary: 05C75: Structural characterization of families of graphs 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.) 05C99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 3 , June 1982 , pp. 289 - 294
Copyright
Copyright © Australian Mathematical Society 1982

References

Cook, C. (1970). Graphs associated with (0, 1) arrays, (Ph.D. Thesis, University of Iowa).Google Scholar
Harary, F., Graph theory (Addison-Wesley, Reading, Mass.).CrossRefGoogle Scholar
Hedetniemi, S. T. and Slater, P. J. (1972), ‘Line graphs of triangleless and iterated clique graph’, Graph theory and applications, edited by Alavi, Y. and Lick, D. R. and White, A. T., pp. 139–147 (Springer-Verlag, Berlin).CrossRefGoogle Scholar