Abstract.
A graph is weakly k-homogeneous if whenever two induced subgraphs on k vertices are isomorphic, then some automorphism of this graph sends one induced subgraph to the other. In this note, we characterize weakly k-homogeneous graphs with certain given number of isolated vertices and given number of nontrivial components. As byproduct, all disconnected weakly k-homogeneous graphs are determined for k=2 and k=3.
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Received: October, 2001 Final version received: October 9, 2002
Acknowledgment. The authors wish to thank the referee for his invaluable remarks.
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Chia, G., Kok, W. A Note on Disconnected Weakly k-Homogeneous Graphs. Graphs Comb 18, 723–729 (2002). https://doi.org/10.1007/s003730200057
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DOI: https://doi.org/10.1007/s003730200057