8 problems

Zero-divisor graph unimodality conjecture. The independence polynomial $I\bigl(\varGamma(\mathbb{Z}_n),x\bigr)$ is unimodal. The paper presents this as a conjecture following compu…

Bender et al.'s conjecture. If $G(S)$ is uniquely complemented with clique number $3$ or greater and every vertex has a unique complement, then $G(S)$ is isomorphic to…

Let $S$ be a finite commutative semigroup with zero, and let $G(S)$ be its zero-divisor graph. A graph is complemented if every vertex is orthogonal to some vertex, where adjacent…

Compressed-graph invariance conjecture. Under these hypotheses,

Compressed-graph structure conjecture. An edge joins the vertices represented by $\"]\phi(\prod_i d_i)$ and $\"]\phi(\prod_i b_i)$ if and only if

GCD-representative conjecture. For every $a\in D$,

Behboodi–Rakeei conjecture. Every reduced ring with more than two minimal primes has annihilating ideal-graph of girth $3$. The paper states that this conjecture is settled by prov…

Beck's conjecture. For every commutative ring $R$ with unity,