On the König deficiency of zero-reducible graphs

On the Structure of Some Deficiency Zero Groups

On the zero forcing number of some Cayley graphs

‎Let Γa be a graph whose each vertex is colored either white or black‎. ‎If u is a black vertex of Γ such that exactly one neighbor‎ ‎v of u is white‎, ‎then u changes the color of v to black‎. ‎A zero forcing set for a Γ graph is a subset of vertices Zsubseteq V(Γ) such that‎ if initially the vertices in Z are colored black and the remaining vertices are colored white‎, ‎then Z changes the col...

On zero-divisor graphs of quotient rings and complemented zero-divisor graphs

For an arbitrary ring $R$, the zero-divisor graph of $R$, denoted by $Gamma (R)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $R$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. It is well-known that for any commutative ring $R$, $Gamma (R) cong Gamma (T(R))$ where $T(R)$ is the (total) quotient ring of $R$. In this...

Reducible properties of graphs

Let IL be the set of all hereditary and additive properties of graphs. For P1,P2 ∈ IL, the reducible property R = P1 ◦ P2 is defined as follows: G ∈ R if and only if there is a partition V (G) = V1 ∪ V2 of the vertex set of G such that 〈V1〉G ∈ P1 and 〈V2〉G ∈ P2. The aim of this paper is to investigate the structure of the reducible properties of graphs with emphasis on the uniqueness of the dec...

On quasi-zero divisor graphs of non-commutative rings

Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,bin R$. The quasi-zero-divisor graph of $R$, denoted by $Gamma^*(R)$ is an undirected graph with all nonzero zero-divisors of $R$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0neq rin R setminus (mathrm{ann}(x) cup mathrm{ann}(y))$ such tha...