﻿ Guoliang Hao

# Guoliang Hao

College of Science, East China University of Technology, Nanchang, P. R. China

## [ 1 ] - The Roman domination and domatic numbers of a digraph

A Roman dominating function (RDF) on a digraph \$D\$ is a function \$f: V(D)rightarrow {0,1,2}\$ satisfying the condition that every vertex \$v\$ with \$f(v)=0\$ has an in-neighbor \$u\$ with \$f(u)=2\$. The weight of an RDF \$f\$ is the value \$sum_{vin V(D)}f(v)\$. The Roman domination number of a digraph \$D\$ is the minimum weight of an RDF on \$D\$. A set \${f_1,f_2,dots,f_d}\$ of Roman dominating functions on ...

## [ 2 ] - 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...