New families of adjointly unique graphs.

*(English)*Zbl 0883.05048The adjoint polynomial \(h(G,x)\) of a graph \(G\) is derived from the chromatic polynomial of its complement. The graph \(G\) is called adjointly unique if \(h(H,x)=h(G,x)\) implies that \(H\) is isomorphic with \(G\). It is clear that a graph is adjointly unique if and only if its complement is chromatically unique. In the paper is presented a class of adjointly unique graphs, which is formed from paths, cycles and \(D_n\) graphs. \(D_n\) is a graph obtained from the union of \(P_{n-2}\) and \(K_3\) by identifying a vertex from \(K_3\) with one endvertex of \(P_{n-2}\).

Reviewer: L.Niepel (Bratislava)

##### MSC:

05C15 | Coloring of graphs and hypergraphs |

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\textit{C. Ye} and \textit{X. Bao}, Discrete Math. 172, No. 1--3, 155--162 (1997; Zbl 0883.05048)

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##### References:

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