an:04200227
Zbl 0727.05023
Koh, K. M.; Teo, K. L.
The search for chromatically unique graphs
EN
Graphs Comb. 6, No. 3, 259-285 (1990).
00156210
1990
j
05C15 05C35
chromatically unique graphs; complete bipartite graphs; chromatic polynomial
Authors' abstract: ``The number of vertex-colourings of a simple graph G in not more than \(\lambda\) colours is a polynomial in \(\lambda\). This polynomial, denoted by P(G,\(\lambda\)), is called the chromatic polynomial of G. A graph G is said to be chromatically unique, in short \(\chi\)- unique, if \(H\cong G\) for any graph H with \(P(H,\lambda)=P(G,\lambda)\). Since the appearance of the first paper on \(\chi\)-unique graphs by \textit{C.-Y. Chao} and \textit{E. J. Whitehead} jun. [Theor. Appl. Graphs, Proc. Kalamazoo 1976, Lect. Notes Math. 642, 121-131 (1978; Zbl 0369.05032)], various families of and several results on such graphs have been obtained successively, especially during the last five years. It is the aim of this expository paper to give a survey on most of the works done on \(\chi\)-unique graphs. A number of related problems and conjectures are also included.''
I.Tomescu (Bucure??ti)
Zbl 0369.05032