This analysis reveals the Seidel Laplacian and signless Laplacian spectrum of weakly zero-divisor graphs, suggesting broader implications for commutative ring theory.
Let us consider the finite commutative ring R, whose unity is 10. The weakly zero-divisor graph, denoted by WΓ(R), is an undirected graph whose distinct vertices c1 and c2 are adjacent if and only if, there exist r ∈ ann(c1) and s ∈ ann(c2) that satisfy the condition rs = 0. This article finds the Seidel Laplacian and Seidel signless Laplacian spectrum for the graph WΓ(Zn) for various values of n.
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Khan et al. (2025) studied this question.
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