﻿ Doost Ali Mojdeh

# Doost Ali Mojdeh

University of Mazandaran

## [ 1 ] - Total double Roman domination in graphs

Let \$G\$ be a simple graph with vertex set \$V\$. A double Roman dominating function (DRDF) on \$G\$ is a function \$f:Vrightarrow{0,1,2,3}\$ satisfying that if \$f(v)=0\$, then the vertex \$v\$ must be adjacent to at least two vertices assigned \$2\$ or one vertex assigned \$3\$ under \$f\$, whereas if \$f(v)=1\$, then the vertex \$v\$ must be adjacent to at least one vertex assigned \$2\$ or \$3\$. The weight of a DR...

## [ 2 ] - 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...

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