Equiprime graph of a seminearring

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.