2025/05/15 by M. Badie, Badie, M., R. Nikandish +3
Mathematics · #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2505.10090
openalex publication_date 2025/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G = (V, E) be a graph with the vertex set V (G) and edge set E(G). The Sombor index of G, SO(G), is defined as ∑uv∈ E(G) √(deg(u)2 + deg(v)2), where deg(u) is the degree of vertex u in V (G). The clean graph of a ring R, denoted by Cl(R), is a graph with vertex set \(e, u) : e ∈ Id(R), u ∈ U(R)\ and two distinct vertices (e, u) and(f, v) are adjacent if and only if ef = 0 or uv = 1 (Id(R) and U(R) are the sets of idempotents and unit elements of R, respectively). The induced subgraph on \(e, u) : e ∈ Id*(R), u ∈ U(R)\ is denoted by Cl2(R). In this paper, SO(Cl2(ℤn)), for different values of the positive integer n, is investigated.