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Volume 11
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Article

The Eigensharp Property for Unit Graphs Associated with Some Finite Rings

by
Heba Adel Abdelkarim
1,
Eman Rawshdeh
2,* and
Edris Rawashdeh
3
1
Department of Mathematics, Irbid National University, Irbid 21110, Jordan
2
Department of Basic Scientific Sciences, Al-Huson University College, Al-Balqa Applied University, Irbid 21110, Jordan
3
Department of Mathematics, Yarmouk University, Irbid 21110, Jordan
*
Author to whom correspondence should be addressed.
Axioms 2022, 11(7), 349; https://doi.org/10.3390/axioms11070349
Submission received: 9 June 2022 / Revised: 6 July 2022 / Accepted: 9 July 2022 / Published: 20 July 2022
(This article belongs to the Special Issue Linear Algebra: Matrix Theory, Graph Theory and Applications)
Review Reports Versions Notes

Abstract

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(Zp) and G(Z2p) are eigensharp graphs. Likewise, we show that the unit graph associated with the ring Zp[x]∕x2 is an eigensharp graph.
Keywords: commutative ring; unit graph; graph join; biclique; biclique partition number; eigensharp graph commutative ring; unit graph; graph join; biclique; biclique partition number; eigensharp graph

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MDPI and ACS Style

Abdelkarim, H.A.; Rawshdeh, E.; Rawashdeh, E. The Eigensharp Property for Unit Graphs Associated with Some Finite Rings. Axioms 2022, 11, 349. https://doi.org/10.3390/axioms11070349

AMA Style

Abdelkarim HA, Rawshdeh E, Rawashdeh E. The Eigensharp Property for Unit Graphs Associated with Some Finite Rings. Axioms. 2022; 11(7):349. https://doi.org/10.3390/axioms11070349

Chicago/Turabian Style

Abdelkarim, Heba Adel, Eman Rawshdeh, and Edris Rawashdeh. 2022. "The Eigensharp Property for Unit Graphs Associated with Some Finite Rings" Axioms 11, no. 7: 349. https://doi.org/10.3390/axioms11070349

APA Style

Abdelkarim, H. A., Rawshdeh, E., & Rawashdeh, E. (2022). The Eigensharp Property for Unit Graphs Associated with Some Finite Rings. Axioms, 11(7), 349. https://doi.org/10.3390/axioms11070349

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