Title : ( Rings whose total graphs have small vertex-arboricity and arboricity )
Authors: morteza Fatehi haghighat , Kazem Khashyarmanesh , Abbas Mohammadian ,
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Abstract
Let R be a commutative ring with non-zero identity, and Z(R) be its set of all zero-divisors. The total graph of R, denoted by T(Γ(R)), is an undirected graph with all elements of R as vertices, and two distinct vertices x and y are adjacent if and only if x + y ∈ Z(R). In this article, we characterize, up to isomorphism, all of finite commutative rings whose total graphs have vertex-arboricity (arboricity) two or three. Also, we show that, for a positive integer v, the number of finite rings whose total graphs have vertex-arboricity (arboricity) v is finite.
Keywords
, total graph, arboricity, vertex-arboricity
@article{paperid:1088122,
author = {Fatehi Haghighat, Morteza and Khashyarmanesh, Kazem and Mohammadian, Abbas},
title = {Rings whose total graphs have small vertex-arboricity and arboricity},
journal = {Hacettepe Journal of Mathematics and Statistics},
year = {2020},
volume = {50},
number = {1},
month = {December},
issn = {1303-5010},
pages = {110--119},
numpages = {9},
keywords = {total graph; arboricity; vertex-arboricity},
}
%0 Journal Article
%T Rings whose total graphs have small vertex-arboricity and arboricity
%A Fatehi Haghighat, Morteza
%A Khashyarmanesh, Kazem
%A Mohammadian, Abbas
%J Hacettepe Journal of Mathematics and Statistics
%@ 1303-5010
%D 2020
