Rose-Hulman Undergraduate Mathematics

Open access Sep 2026

A Poset-Theoretic Approach to Reduced Cozero-Divisor Graphs of ℤ n and Related Rings

Let R be a finite commutative ring with identity, and let Γ′ᵣ(R) denote its reduced cozero-divisor graph. We organize Γ′ᵣ(R) through the poset Prin*(R) of nonzero proper principal ideals and prove that adjacency is exactly incomparability in this poset. Consequently, cliques correspond to antichains, independent sets c...

Dong-Ze Du · Theoretical and Natural Scie... · 0 citations

Open access 2026

Graph Energy of Ideal-Based Zero-Divisor Graphs.

Let R be a finite commutative ring with identity and let I be a proper ideal of R. The ideal-based zero-divisor graph \Gamma_I(R) has vertices outside I that annihilate some element outside I modulo I, with x adjacent to y whenever xy\in I. This paper studies the adjacency energy of \Gamma_I(R). General trace bounds ar...

Rosalio G. Artes, R. Malalay, M. Mbah et al. · International Journal of Mat... · 0 citations

Preprint Aug 2026

Boxicity and Threshold Dimension of Zero Divisor Graphs

The zero divisor graph $\Gamma(R)$ of a finite commutative ring $R$ has as vertices the non-zero zero divisors of $R$, with an edge between two elements exactly when their product is zero. We determine the boxicity and threshold dimension of $\Gamma(R)$ for two classes of finite commutative rings: reduced rings and quo...

Marco Caoduro, Meike Neuwohner · 0 citations

Open access 2026

Directed graphs defined by prime divisors of polynomial values

Let L be the class of all nonconstant polynomials f(x) == Ax2 + Bx + C ∈ Z[x], which are not of the forms Ax2, Bx. We consider the directed graph Gf whose vertex set is P and p → q iff q | f(p), p ̸= q. Let Lf (p) be the set of simple directed paths starting at p and ℓf (p) = sup{|L| : L ∈ Lf (p)}, where |L| is the num...

I. Kátai, P. Bui · Annales Universitatis Scient... · 0 citations

Preprint Sep 2026

Sharp bounds for intervals in finite subgroup lattices

Let H be a subgroup of a finite group G, and put n = [G:H]>1. If p is the least prime divisor of n, we prove that the number of subgroups K with H<= K<= G is less than c(p) n^((log_p n)/4). Here c(p) is the product of (1 - p^(-j))^(-1) over all positive integers j, multiplied by the sum of p^(-z^2) over all integers z....

S. Palcoux, Pablo Spiga · 0 citations

Preprint Sep 2026

So's Conjecture for Integral Circulant Graphs of Order p^aq

So conjectured that, for a fixed positive integer n, the ordinary adjacency spectrum of an integral circulant graph of order n determines its divisor set. We prove this for graphs of order p to the power a times q, where p and q are primes with p less than q and a is at least one. To handle coincident eigenvalues arisi...

Jian-Wei Jiang, Chun-Hua Yang · 0 citations