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Chromatic classes of certain 2-connected $$(n,n+2)$$-graphs. (English) Zbl 0760.05044
Let $${\mathcal S}$$ denote the class of 2-connected graphs with order $$n$$ and size $$n+2$$ which contain either a 4-cycle without chords or two triangles. There are determined all equivalence classes in $${\mathcal S}$$ under the equivalence relation “two graphs are chromatically equivalent if they have the same chromatic polynomial”. The authors show that three of nine classes are classes of chromatically unique graphs.
Reviewer: J.Fiamcik

MSC:
 05C15 Coloring of graphs and hypergraphs 05C75 Structural characterization of families of graphs 05C35 Extremal problems in graph theory