Strong Resolving Graphs of U-Clean Graphs of Finite Commutative Rings

Ziyi Wu and Xiaobin Yin

Journal of Mathematics, 2026, vol. 2026, 1-7

Abstract: Let R be a finite commutative ring with identity 1. The U-clean graph U-ClR of a ring R is a simple undirected graph with vertices are of the form e,u, where e is a nonzero idempotent and u is a unit of R, and two distinct vertices e,u, f,v of U-ClR are adjacent if and only if e=f=1 or uv=1. In this paper, we present the strong resolving graph U-ClRSR of U-ClR. The vertex degrees, the independence number, the clique number, and the chromatic number of U-ClRSR are determined. Moreover, we show that if k is a divisor of n−1n, where k and n are positive integers with k>n≥3, then U-ClZk is not a complete graph. Finally, we give some examples of U-ClZn and U-ClSRZn to illustrate our results.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2925466

DOI: 10.1155/jom/2925466

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