The Eigensharp Property for Unit Graphs Associated with Some Finite Rings - Heba Adel Abdelkarim; Eman Rawshdeh; Edris Rawashdeh (Axioms, 2022)
Let R be a commutative ring with unity. The unit graph <semantics>G(R)</semantics> is defined such that the vertex set of <semantics>G(R)</semantics> is the set of all elements of R, and two distinct vertices are adjacent if their sum is a unit in <semantics>R.</semantics> In this paper, we show that for each prime, <semantics>p,G(Zp)</semantics> and <semantics>G(Z2p)</semantics> are eigensharp graphs. Likewise, we show that the unit graph associated with the ring <semantics>Zp[x]∕<mfenced separators="" open="⟨" close="⟩">x2</mfenced></semantics> is an eigensharp graph.