Line Graph associated with Equiprime Graph of a Nearring

Sabina Rachana Crasta; Jagadeesha B

doi:10.5269/bspm.80058

Sabina Rachana Crasta St Joseph Engineering College, Vamanjoor, Mangaluru, Karnataka India 575028
Jagadeesha B St Joseph Engineering College, Vamanjoor Mangaluru

Abstract

This paper presents a graph-theoretic exploration of three nearring-based graphs—namely, the generalized graph GI (N), the equiprime graph EQI (N), and the central graph CI (N)—each defined with respect to a fixed ideal I of a nearring N. Focusing on their respective line graphs, we analyze the structural changes that emerge when the original adjacency is lifted to edge adjacencies. The motivation stems from recent advances in algebraic graph theory, where such constructions have yielded insights into ideal-related interactions within algebraic systems. Through theoretical results and illustrative examples, we demonstrate how the line graph of the equiprime graph captures nuanced connectivity patterns and contributes to a finer
classification of algebraic elements. This unified approach reveals new perspectives on how algebraic structure influences graph-theoretic behavior.

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