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8 pages, 267 KiB

Open AccessArticle

by Heba Adel Abdelkarim, Eman Rawshdeh and Edris Rawashdeh

Axioms 2022, 11(7), 349; https://doi.org/10.3390/axioms11070349 - 20 Jul 2022

Cited by 3 | Viewed by 1839

Let R be a commutative ring with unity. The unit graph

G (R)

is defined such that the vertex set of

G (R)

is the set of all elements of R, and two distinct vertices are adjacent if [...] Read more.

Let R be a commutative ring with unity. The unit graph

G (R)

is defined such that the vertex set of

G (R)

is the set of all elements of R, and two distinct vertices are adjacent if their sum is a unit in

R .

In this paper, we show that for each prime,

p, G (Z_{p})

and

G (Z_{2 p})

are eigensharp graphs. Likewise, we show that the unit graph associated with the ring

^{Z_{p} [x]} ∕_{⟨x^{2}⟩}

is an eigensharp graph. Full article

(This article belongs to the Special Issue Linear Algebra: Matrix Theory, Graph Theory and Applications)

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