## [ 1 ] - Total \$k\$-Rainbow domination numbers in graphs

Let \$kgeq 1\$ be an integer, and let \$G\$ be a graph. A {it\$k\$-rainbow dominating function} (or a {it \$k\$-RDF}) of \$G\$ is afunction \$f\$ from the vertex set \$V(G)\$ to the family of all subsetsof \${1,2,ldots ,k}\$ such that for every \$vin V(G)\$ with\$f(v)=emptyset \$, the condition \$bigcup_{uinN_{G}(v)}f(u)={1,2,ldots,k}\$ is fulfilled, where \$N_{G}(v)\$ isthe open neighborhood of \$v\$. The {it weight} o...

## [ 2 ] - The sum-annihilating essential ideal graph of a commutative ring

Let \$R\$ be a commutative ring with identity. An ideal \$I\$ of a ring \$R\$is called an annihilating ideal if there exists \$rin Rsetminus {0}\$ such that \$Ir=(0)\$ and an ideal \$I\$ of\$R\$ is called an essential ideal if \$I\$ has non-zero intersectionwith every other non-zero ideal of \$R\$. Thesum-annihilating essential ideal graph of \$R\$, denoted by \$mathcal{AE}_R\$, isa graph whose vertex set is the set...

## [ 3 ] - Some properties and domination number of the complement of a new graph associated to a commutative ring

In this paper some properties of the complement of  a new graph  associated with a commutative ring  are investigated ....

نویسندگان همکار