Shahrood University of Technology

## [ 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 ] - On Hop Roman Domination in Trees

‎Let \$G=(V,E)\$ be a graph‎. ‎A subset \$Ssubset V\$ is a hop dominating set‎‎if every vertex outside \$S\$ is at distance two from a vertex of‎‎\$S\$‎. ‎A hop dominating set \$S\$ which induces a connected subgraph‎ ‎is called a connected hop dominating set of \$G\$‎. ‎The‎‎connected hop domination number of \$G\$‎, ‎\$ gamma_{ch}(G)\$,‎‎‎ ‎is the minimum cardinality of a connected hop‎‎dominating set of \$G\$...

## [ 3 ] - Bounds on the outer-independent double Italian domination number

An outer-independent double Italian dominating function (OIDIDF)on a graph \$G\$ with vertex set \$V(G)\$ is a function\$f:V(G)longrightarrow {0,1,2,3}\$ such that if \$f(v)in{0,1}\$ for a vertex \$vin V(G)\$ then \$sum_{uin N[v]}f(u)geq3\$,and the set \$ {uin V(G)|f(u)=0}\$ is independent. The weight ofan OIDIDF \$f\$ is the value \$w(f)=sum_{vin V(G)}f(v)\$. Theminimum weight of an OIDIDF on a graph \$G\$ is cal...

## [ 4 ] - Total domination in cubic Knodel graphs

A subset D of vertices of a graph G is a dominating set if for each u ∈ V (G) \ D, u is adjacent to somevertex v ∈ D. The domination number, γ(G) ofG, is the minimum cardinality of a dominating set of G. A setD ⊆ V (G) is a total dominating set if for eachu ∈ V (G), u is adjacent to some vertex v ∈ D. Thetotal domination number, γt (G) of G, is theminimum cardinality of a total dominating set o...

## [ 5 ] - Strength of strongest dominating sets in fuzzy graphs

A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of \$G\$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...

نویسندگان همکار