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Some new results on Jacobson graphs

  • Z. Fattahi
  • A. ErfanianEmail author
  • M. Alinejad
Article
  • 17 Downloads

Abstract

Let R be a commutative ring with non-zero identity, and J(R) be the Jacobson ideal of R. The Jacobson graph of R is a graph with vertex set \(R {\setminus } J(R),\) and two distinct vertices x and y are adjacent if and only if \(1-xy \) is not a unit element. In this paper we characterize the finite Jacobson graphs which are chordal graphs, cographs, line graphs, or interval graphs. Among other results, we find the degree set of finite Jacobson graphs, and the number of vertices with specific degree.

Keywords

Jacobson graph Chordal graph Cograph Line graph Degree set 

Mathematics Subject Classification

Primary 05C10 05C69 Secondary 16P10 16N20 

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Pure MathematicsFerdowsi University of MashhadMashhadIran
  2. 2.Department of Pure Mathematics and the Center of Excelence in Analysis on Algebraic StructuresFerdowsi University of MashhadMashhadIran

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