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Some new results on Jacobson graphs

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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.

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Authors and Affiliations

  1. Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

    Z. Fattahi & M. Alinejad

  2. Department of Pure Mathematics and the Center of Excelence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, Iran

    A. Erfanian

Authors
  1. Z. Fattahi
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  2. A. Erfanian
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  3. M. Alinejad
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Correspondence to A. Erfanian.

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Fattahi, Z., Erfanian, A. & Alinejad, M. Some new results on Jacobson graphs. Rend. Circ. Mat. Palermo, II. Ser 68, 129–137 (2019). https://doi.org/10.1007/s12215-018-0343-0

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  • DOI: https://doi.org/10.1007/s12215-018-0343-0

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