Weakly Perfect Graphs of Modules

Document Type : بنیادی - نظری


1 Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697 Tehran, Iran

2 Department of Mathematics University of Mazandaran Babolsar, Iran

3 Department of Mathematics, Payame Noor University (PNU) Tehran, Iran



In this study‎, ‎$R$ and $M$ are assumed to be a commutative ring with non-zero identity $M$ and an $R$-module‎, ‎respectively‎. ‎Scalar Product Graph of $M$‎, ‎denoted by $G_R(M)$‎, ‎is a graph with the vertex-set $M$ and two different vertices $a$ and $b$ in $M$ are connected if and only if there exists $r$ belong to $R$ such that $a=rb$ or $b=ra$‎. ‎This paper studies some properties of such weakly perfect graphs‎.


Main Subjects

bibitem{afkhami} Afkhami M.‎, ‎Khashyarmanesh K‎. ‎(2011)‎. ‎``The cozero-divisor graph of a commutative ring''‎, ‎Southeast Asian Bulletin of Mathematics‎, ‎35‎, ‎753-762‎.
‎bibitem{alibemani} Alibemani A.‎, ‎Hashemi E.‎, ‎Alhevaz A‎. ‎(2018)‎. ‎``The cozero-divisor graph of a module''‎, ‎Asian-European Journal of Mathematics‎, ‎11‎, ‎DOI‎: ‎10.1142/S1793557118500924‎.
‎bibitem{fander} Fander M.R‎. ‎(2015)‎. ‎``Chromatic and clique number of a class of perfect graph''‎, ‎Transactions on Combinatorics‎, ‎4‎, ‎1-4‎.
‎bibitem{Maimani} Maimani H.R.‎, ‎Pournaki M.R.‎, ‎Yassemi S‎. ‎(2010)‎. ‎``A class of weakly perfect graphs''‎, ‎Czechoslovak Mathematical Journal‎, ‎60‎, ‎1037-1041‎.
‎bibitem{nikandish} Nikandish R.‎, ‎Maimani H.R.‎, ‎Izanloo H‎. ‎(2016)‎. ‎``The annihilating-ideal graph of $Z_n$ is weakly perfect''‎, ‎Contributions to Discrete Mathematics 11‎, ‎16-21‎.
‎bibitem{noori1} Nouri Jouybari M.‎, ‎Talebi Y.‎, ‎Firouzian S‎. ‎(2019)‎. ‎``Scalar Product Graphs of Modules''‎, ‎International Journal of Nonlinear Analysis and Applications‎, ‎10‎, ‎Special Issue (Nonlinear Analysis in Engineering and Sciences)‎, ‎75-82‎.
‎bibitem{wiener} Wiener H‎. ‎(1947)‎. ‎``Structural Determination of Paraffin Boiling Points''‎, ‎Journal American Chemistry Society‎, ‎69‎, ‎17-20‎.
‎bibitem{gutman} Yeh Y.‎, ‎Gutman I‎. ‎(1994)‎. ‎``On the some of all Distances in Composite Graphs''‎, ‎Discrete Mathematics‎, ‎135‎, ‎359-365‎.