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Some families of chromatically unique bipartite graphs. (English) Zbl 0958.05054
Summary: A graph is said to be chromatically unique (or \(\chi\)-unique) if it is uniquely determined by its chromatic polynomial. Let \(K^{-r}(p,q)\) denote the family of graphs obtained from \(K_{p,q}\) by deleting any \(r\) distinct edges. In this paper, we study the chromaticity of the graphs in \(K^{-r}(p,q)\). A sufficient condition is given for a member of \(K^{-r}(p,q)\) to be \(\chi\)-unique and some families of \(\chi\)-unique bipartite graphs are obtained. A conjecture is also proposed.
MSC:
05C15 Coloring of graphs and hypergraphs
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