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New families of adjointly unique graphs. (English) Zbl 0883.05048
The 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 \(P_{n-2}\).
MSC:
05C15 Coloring of graphs and hypergraphs
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References:
[1] Ru-Ying, Liu, A new method to find chromatic polynomial of graph and its applications, Kexue tongbao, 32, 1508-1509, (1987)
[2] Ru-Ying, Liu, Chromatic uniqueness of complement of the irreducible cycles union, Mathematica applicata, 7, 200-205, (1994)
[3] Ru-Ying, Liu, On chromatic polynomials of two classes of graphs, Kexue tongbao, 32, 1147-1148, (1987)
[4] Ru-Ying, Liu, Chromatic uniqueness of a kind of graph, J. neimenggu univ., 25, 469-475, (1994) · Zbl 1333.05118
[5] Ru-Ying, Liu, Chromatic uniqueness of Kn − E(kps ∪ rpt), J. systems sci. math. sci., 12, 207-214, (1992)
[6] Ru-Ying, Liu, Several results on adjoint polynomials of graphs, J. qinghai normal univ., 1, 1-6, (1992)
[7] Ru-Ying, Liu, Chromatic uniqueness of complementary graph of Pq − 1, J. math. res. exposition, 14, 469-472, (1994) · Zbl 0882.05066
[8] Liu Ru-Ying and Chen Zi-Qi, Two new classes of chromatically unique graphs, J. Neimenggu Univ., to appear.
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