A generalization of commuting graphs
Author:
, , , , ,Year
: 2014
Abstract: Let R be a ring with the identity element 1, α be an endomorphism of R and b be a
left α-derivation. In this paper, we introduce a generalization of a commuting graph,
which is denoted by ΓR(α, b), as a directed graph with vertex set R and, for two distinct
vertices x and y, there is an arc from x to y if and only if xy = α(y)x + b(y). We study
some basic properties of ΓR(α, b). Also, we investigate the planarity and genus of the
graph ΓR(α, 0).
left α-derivation. In this paper, we introduce a generalization of a commuting graph,
which is denoted by ΓR(α, b), as a directed graph with vertex set R and, for two distinct
vertices x and y, there is an arc from x to y if and only if xy = α(y)x + b(y). We study
some basic properties of ΓR(α, b). Also, we investigate the planarity and genus of the
graph ΓR(α, 0).
Keyword(s): Commuting graph,derivation,planar graph,genus
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A generalization of commuting graphs
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| contributor author | Mojgan Afkhami | en |
| contributor author | Zahra Barati | en |
| contributor author | سیده نسا حسینی | en |
| contributor author | کاظم خشیارمنش | en |
| contributor author | Seyede Nesa Hoseini | fa |
| contributor author | Kazem Khashyarmanesh | fa |
| date accessioned | 2020-06-06T13:22:58Z | |
| date available | 2020-06-06T13:22:58Z | |
| date issued | 2014 | |
| identifier uri | http://libsearch.um.ac.ir:80/fum/handle/fum/3352596?locale-attribute=en | |
| description abstract | Let R be a ring with the identity element 1, α be an endomorphism of R and b be a left α-derivation. In this paper, we introduce a generalization of a commuting graph, which is denoted by ΓR(α, b), as a directed graph with vertex set R and, for two distinct vertices x and y, there is an arc from x to y if and only if xy = α(y)x + b(y). We study some basic properties of ΓR(α, b). Also, we investigate the planarity and genus of the graph ΓR(α, 0). | en |
| language | English | |
| title | A generalization of commuting graphs | en |
| type | Journal Paper | |
| contenttype | External Fulltext | |
| subject keywords | Commuting graph | en |
| subject keywords | derivation | en |
| subject keywords | planar graph | en |
| subject keywords | genus | en |
| journal title | Discrete Mathematics, Algorithms and Applications | fa |
| pages | 145006801-145006811 | |
| journal volume | 7 | |
| journal issue | 1 | |
| identifier link | https://profdoc.um.ac.ir/paper-abstract-1046570.html | |
| identifier articleid | 1046570 |