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<p>Let <i>R</i> be a commutative ring with identity. The involutory Cayley graph <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {G}(R)\)</EquationSource> </InlineEquation> of <i>R</i> is defined as the graph whose vertex set is the set of elements of <i>R</i>, where two vertices <i>a</i> and <i>b</i> are adjacent exactly when <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((a-b)^2=1\)</EquationSource> </InlineEquation>. This paper investigates the properties of involutory Cayley graphs associated with polynomial and power series rings over the ring of integers modulo <i>n</i>.</p>

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Involutory Cayley Graphs of Polynomial and Power Series Rings Over the Ring of Integers Modulo n

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Hamide Keshavarzi,
  • Afshin Amini,
  • Babak Amini

摘要

Let R be a commutative ring with identity. The involutory Cayley graph \(\mathcal {G}(R)\) of R is defined as the graph whose vertex set is the set of elements of R, where two vertices a and b are adjacent exactly when \((a-b)^2=1\) . This paper investigates the properties of involutory Cayley graphs associated with polynomial and power series rings over the ring of integers modulo n.