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The strongly asymmetric graphs of order 6 and 7. (English) Zbl 0808.05074

Summary: Let \(G\) be an arbitrary connected simple graph of order \(n\). \(G\) is called a strongly asymmetric graph if all induced overgraphs of \(G\) of order \(n+1\) are nonisomorphic. We give a list of all strongly asymmetric graphs of order \(6\) and \(7\). Also we prove that there exist exactly 16 asymmetric graphs of order \(7\) which are not strongly asymmetric.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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