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Information Journal Paper

Title

Toroidality and Projectivity index of Jacobson Graph

Pages

  61-74

Abstract

 Given a graph Г , we denote the kth Iterated line graph of Г by LK(Г ) and LK(Г )=L(LK-1(Г )). In particular, L0(Г )=Г and L1(Г )=L(Г ) is the line graph of Г . The toroidality (and projectivity) index of a graph Г is the smallest integer k such that the kth Iterated line graph of Г is non-toroidal (and non-projective). We denote the Toroidality index of a graph Г by ξ T and the Projectivity index of a graph Г by ξ P. If LK(Г ) is toroidal (and projective) for all k≥ 0, we define ξ T=∞ (and ξ P=∞ ). Let R be a commutative ring with nonzero identity. Then the Jacobson graph of R, denoted by 𝔍 R, is defined as a simple graph with vertex set RJ(R) such that two distinct vertices x and y are adjacent if and only if 1-xy is not a unit of R. In this paper, we study the toroidality and projectivity indices of Jacobson graphs. We give full characterization of this graph with respect to its toroidality and projectivity indices. Moreover, the toroidality and Projectivity index of Jacobson graph is either infinite or two.

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    APA: Copy

    Parsapour, Atossa, & Ahmad Javaheri, Khadijeh. (2021). Toroidality and Projectivity index of Jacobson Graph. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 7(30 ), 61-74. SID. https://sid.ir/paper/953448/en

    Vancouver: Copy

    Parsapour Atossa, Ahmad Javaheri Khadijeh. Toroidality and Projectivity index of Jacobson Graph. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2021;7(30 ):61-74. Available from: https://sid.ir/paper/953448/en

    IEEE: Copy

    Atossa Parsapour, and Khadijeh Ahmad Javaheri, “Toroidality and Projectivity index of Jacobson Graph,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 7, no. 30 , pp. 61–74, 2021, [Online]. Available: https://sid.ir/paper/953448/en

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