Name
Abstract | ||
|---|---|---|
The study of chromatically unique graphs has been drawing much attention and many results are surveyed in [4, 12, 13]. The notion of adjoint polynomials of graphs was first introduced and applied to the study of the chromaticity of the complements of the graphs by Liu [17] (see also [4]). Two invariants for adjoint equivalent graphs that have been employed successfully to determine chromatic unique graphs were introduced by Liu [17] and Dong et al. [4] respectively. In the paper, we shall utilize, among other things, these two invariants to investigate the chromaticity of the complement of the tadpole graphs C-n(P-m), the graph obtained from a path P-m and a cycle C-n by identifying a pendant vertex of the path with a vertex of the cycle. Let (G) over bar stand for the complement of a graph G. We prove the following results: 1. The graph <(Cn-1(P-2))over bar> is chromatically unique if and only if n not equal 5, 7. 2. Almost every <(C-n(P-m))over bar> is not chromatically unique, where n >= 4 and m >= 2. |
Year | DOI | Venue |
|---|---|---|
2013 | null | ARS COMBINATORIA |
Keywords | Field | DocType |
chromatic polynomials,chromatically unique,adjoint polynomials,adjointly unique,characters | Discrete mathematics,Indifference graph,Combinatorics,Vertex (geometry),Chromatic scale,Polynomial,Chordal graph,Invariant (mathematics),Pathwidth,Mathematics,Complement graph | Journal |
Volume | Issue | ISSN |
108 | null | 0381-7032 |
Citations | PageRank | References |
0 | 0.34 | 6 |
Authors | ||
6 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. F. Wang | 1 | 0 | 0.34 |
| Xiaoqi Huang | 2 | 10 | 3.52 |
| K. L. Teo | 3 | 1643 | 211.47 |
| Francesco Belardo | 4 | 15 | 8.54 |
| R. Y. Liu | 5 | 0 | 0.34 |
| C. F. Ye | 6 | 0 | 0.34 |