Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T06:14:02.520Z Has data issue: false hasContentIssue false

WEAKLY PERFECT GRAPHS ARISING FROM RINGS

Published online by Cambridge University Press:  22 March 2010

H. R. MAIMANI
Affiliation:
Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, PO Box 16785-163, Tehran, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran. e-mail: [email protected]
M. R. POURNAKI
Affiliation:
Department of Mathematical Sciences, Sharif University of Technology, PO Box 11155-9415, Tehran, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran. e-mail: [email protected], http://math.ipm.ac.ir/pournaki/
S. YASSEMI
Affiliation:
School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran. email: [email protected], http://math.ipm.ac.ir/yassemi/
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A graph is called weakly perfect if its chromatic number equals its clique number. In this paper a new class of weakly perfect graphs arising from rings are presented and an explicit formula for the chromatic number of such graphs is given.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Ashrafi, N., Maimani, H. R., Pournaki, M. R. and Yassemi, S., Unit graphs associated with rings, Comm. Algebra, to appear.Google Scholar
2.Atiyah, M. F. and Macdonald, I. G., Introduction to Commutative Algebra (Addison Wesley, Reading, MA.–London–Don Mills, ON, 1969).Google Scholar
3.Grimaldi, R. P., Graphs from rings, in Proceedings of the Twentieth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1989). Congr. Numer. 71 (1990), 95103.Google Scholar
4.McDonald, B. R., Finite rings with identity, in Pure and Applied Mathematics, vol. 28 (Marcel Dekker, Inc., New York, 1974).Google Scholar
5.West, D. B., Introduction to Graph Theory (Prentice Hall, Upper Saddle River, NJ, 1996).Google Scholar