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On q-trees. (English) Zbl 0591.05021
A q-tree is defined inductively as a complete graph $$K_ q$$ on q vertices or as the graph G’ obtained from a q-tree G by adding a new vertex that is adjacent to all the vertices in some $$K_ q$$ of G. The authors show that the chromatic polynomial $$P(G,\lambda)$$ of a q-tree with n vertices $$(n\geq q)$$ is $$P(G,\lambda)=\lambda (\lambda - 1)...(\lambda -q+1)(\lambda -q)^{n-q}.$$
Reviewer: A.Tucker

##### MSC:
 05C05 Trees 05C15 Coloring of graphs and hypergraphs 05C35 Extremal problems in graph theory
##### Keywords:
q-tree; chromatic polynomial
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##### References:
 [1] Graph Theory. Addison-Wesley, Reading, MA (1969). [2] Read, J. Combinatorial Theory 4 pp 52– (1968) · Zbl 0165.32802 [3] Stirling numbers and coloring of q-trees, Prace Nauk. Inst. Mat. Politechn. Wroclaw, Ser. Stud. i Materiý 13, Grafy, hipergrafy, system blokow (1977), pp. 63–67. [4] Whitehead, J. Graph Theory 9 pp 279– (1985)
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