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<p>Defining a graph that establishes a connection between ring theory and graph theory is an interesting area of research in mathematics. In this paper, we establish a relationship between graphs and seminearrings, which are generalizations of rings. We propose an equiprime graph of a seminearring <i>S</i>, which handles both the binary operations of <i>S</i>. It’s interesting to see that the classical zero-divisor graph is a special case of an equiprime (e-prime) graph. Further, other prime graphs are studied in detail, and related results are presented. Additionally, we examine the conditions under which the ideal becomes a vertex cover of the e-prime graph and the dominating set of its line graph.</p>

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Equiprime graph of a seminearring

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月22日

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  • Prakash Padoor,
  • Babushri Srinivas Kedukodi,
  • Syam Prasad Kuncham,
  • Kavitha Koppula

摘要

Defining a graph that establishes a connection between ring theory and graph theory is an interesting area of research in mathematics. In this paper, we establish a relationship between graphs and seminearrings, which are generalizations of rings. We propose an equiprime graph of a seminearring S, which handles both the binary operations of S. It’s interesting to see that the classical zero-divisor graph is a special case of an equiprime (e-prime) graph. Further, other prime graphs are studied in detail, and related results are presented. Additionally, we examine the conditions under which the ideal becomes a vertex cover of the e-prime graph and the dominating set of its line graph.