# The chromaticity of a family of 2-connected 3-chromatic graphs with five triangles and cyclomatic number six

Discussiones Mathematicae Graph Theory (1998)

- Volume: 18, Issue: 1, page 99-111
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topHalina Bielak. "The chromaticity of a family of 2-connected 3-chromatic graphs with five triangles and cyclomatic number six." Discussiones Mathematicae Graph Theory 18.1 (1998): 99-111. <http://eudml.org/doc/270193>.

@article{HalinaBielak1998,

abstract = {In this note, all chromatic equivalence classes for 2-connected 3-chromatic graphs with five triangles and cyclomatic number six are described. New families of chromatically unique graphs of order n are presented for each n ≥ 8. This is a generalization of a result stated in [5]. Moreover, a proof for the conjecture posed in [5] is given.},

author = {Halina Bielak},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {chromatically equivalent graphs; chromatic polynomial; chromatically unique graphs; cyclomatic number; chromatic equivalence; chromatic number; chromaticity},

language = {eng},

number = {1},

pages = {99-111},

title = {The chromaticity of a family of 2-connected 3-chromatic graphs with five triangles and cyclomatic number six},

url = {http://eudml.org/doc/270193},

volume = {18},

year = {1998},

}

TY - JOUR

AU - Halina Bielak

TI - The chromaticity of a family of 2-connected 3-chromatic graphs with five triangles and cyclomatic number six

JO - Discussiones Mathematicae Graph Theory

PY - 1998

VL - 18

IS - 1

SP - 99

EP - 111

AB - In this note, all chromatic equivalence classes for 2-connected 3-chromatic graphs with five triangles and cyclomatic number six are described. New families of chromatically unique graphs of order n are presented for each n ≥ 8. This is a generalization of a result stated in [5]. Moreover, a proof for the conjecture posed in [5] is given.

LA - eng

KW - chromatically equivalent graphs; chromatic polynomial; chromatically unique graphs; cyclomatic number; chromatic equivalence; chromatic number; chromaticity

UR - http://eudml.org/doc/270193

ER -

## References

top- [1] C.Y. Chao and E.G. Whitehead Jr., Chromatically unique graphs, Discrete Math. 27 (1979) 171-177, doi: 10.1016/0012-365X(79)90107-9. Zbl0411.05035
- [2] K.M. Koh and C.P. Teo, The search for chromatically unique graphs, Graphs and Combinatorics 6 (1990) 259-285, doi: 10.1007/BF01787578. Zbl0727.05023
- [3] K.M. Koh and C.P. Teo, The chromatic uniqueness of certain broken wheels, Discrete Math. 96 (1991) 65-69, doi: 10.1016/0012-365X(91)90471-D. Zbl0752.05029
- [4] F. Harary, Graph Theory (Reading, 1969).
- [5] N-Z. Li and E.G. Whitehead Jr., The chromaticity of certain graphs with five triangles, Discrete Math. 122 (1993) 365-372, doi: 10.1016/0012-365X(93)90312-H. Zbl0787.05040
- [6] R.C. Read, An introduction to chromatic polynomials, J. Combin. Theory 4 (1968) 52-71, doi: 10.1016/S0021-9800(68)80087-0. Zbl0173.26203

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.