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Another family of chromatically unique graphs. (English) Zbl 0836.05028
A graph $$G$$ is chromatically unique if any graph that has the same chromatic polynomial as $$G$$ is isomorphic to $$G$$. There are several classes of graphs that are known to be chromatically unique. In this paper the author presents a construction that provides a new family of chromatically unique graphs.
Reviewer: M.Frick (Pretoria)

##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
##### Keywords:
chromatic polynomial; chromatically unique graphs
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##### References:
 [1] Chao, C.Y., Whitehead Jr., E.G.; On the chromatic equivalence of graphs, Lecture Notes in Math.642, Springer-Verlag, New York 121–131 (1978) [2] Chao, C.Y., Zhao, L.C.; Chromatic polynomials of a family of graphs, Ars Combinatoria15, 111–129 (1983) · Zbl 0532.05027 [3] Chia, G.L.; Personal communication [4] Loerinc, B.; Chromatic Uniqueness of the generalized$$\theta$$-graph, Discrete Math.23, 313–316 (1979) · Zbl 0389.05034 [5] Koh, K.M., Teo, K.L.; The search for chromatically unique graphs, Graphs and Combinatorics6, 259–285 (1990) · Zbl 0727.05023 · doi:10.1007/BF01787578 [6] Peng, Y.H.; New infinite families of chromatically unique graphs, Sains Malaysiana (Quantitative Studies)21(4, 15–25 (1992) [7] Read, R.C.; Broken Wheel are SLC, Ars Combinatoria21-A, 123–128 (1986) · Zbl 0597.05033 [8] —-; An introduction to chromatic polynomials, J. Combinatorial Theory4, 52–71 (1968) · Zbl 0173.26203 · doi:10.1016/S0021-9800(68)80087-0 [9] Xu, S.J., Liu, J.J., Peng, Y.H.; The chromaticity ofs-bridge graphs and related graphs, Discrete Mathematics (to be published) · Zbl 0814.05036
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