zbMATH — the first resource for mathematics

Chromatic uniqueness of the complements of certain forests. (English) Zbl 0878.05031
A \(T\)-shape tree is a tree with the degree sequence \(\{ 1,1,1,2,2,\dots, 2,3\}\). By studying adjoint polynomials, the authors obtained the following result. There is a family \(\mathcal H\) of \(T\)-shape trees such that for each \(H \in {\mathcal H}\), if the complement of a graph \(G\) is a disjoint union of any number of copies of \(H\), then \(G\) is chromatically unique.
05C15 Coloring of graphs and hypergraphs
05C05 Trees
Full Text: DOI
[1] Koh, K.M.; Teo, K.L., The search for chromatically unique graphs, Graph combin., 6, 259-285, (1990) · Zbl 0727.05023
[2] Liu, Ru-Ying, On chromatic polynomials of two classes of graphs, Kexue tongbao, 32, 16, 1147-1148, (1987)
[3] Liu, Ru-Ying, Adjoint polynomial of graphs, J. qinghai normal univ., 3, 1-9, (1990)
[4] Liu, Ru-Ying, Chromatic uniqueness of \(Kn — E(kPs ⊎ rPt)\), J. system sci. math. sci., 12, 3, 207-214, (1992)
[5] Liu, Ru-Ying, Several results on adjoint polynomial of graphs, J. qinghai normal univ., 1, 1-6, (1992)
[6] Liu, Ru-Ying, Chromatic uniqueness of a kind of graph, J. neimenggu univ., 25, 5, 469-475, (1994) · Zbl 1333.05118
[7] Liu, Ru-Ying, Chromatic uniqueness of complementary graphs of a kind of tree, Math. appl. supplement, 9, 170-173, (1996)
[8] Zhou, Bo-Xun, Higher algebra, (1966), The People’s Educational Publishing House Beijing
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.