Title : ( On the genus of graphs associated to a commutative ring )
Authors: Kazem Khashyarmanesh , Mahdi Reza Khorsandi ,
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Abstract
Let T( Gamma(R)) be the total graph of a commutative ring R , that is a graph with all elements of R as vertices and two distinct vertices a and b are adjacent if and only if a+b is a zero-divisor on R . In this talk, we classify all finite rings R whose total graphs T( Gamma(R)) are projective. Also, we present a survey on some recent research on the genus of graphs associated to a commutative ring.
Keywords
, Planar graph, Total graph, Projective graph-Crosscap number, Zero-divisor graph
@inproceedings{paperid:1020719,
author = {Khashyarmanesh, Kazem and Khorsandi, Mahdi Reza},
title = {On the genus of graphs associated to a commutative ring},
booktitle = {Third Algebraic Combinatorics Conference of Iran 2011},
year = {2011},
location = {اصفهان, IRAN},
keywords = {Planar graph;Total graph; Projective graph-Crosscap number; Zero-divisor graph},
}
%0 Conference Proceedings
%T On the genus of graphs associated to a commutative ring
%A Khashyarmanesh, Kazem
%A Khorsandi, Mahdi Reza
%J Third Algebraic Combinatorics Conference of Iran 2011
%D 2011
