A Roman dominating function on a graph G=(V, E) is a function f: V→{0, 1, 2} satisfying the
condition that every vertex u for which f (u)= 0 is adjacent to at least one vertex v for which f …

This chapter is concerned with the concept Roman domination in graphs, which was
introduced in 2004 by Cockayne, Dreyer, SM Hedetniemi, and ST Hedetniemi based on the …

Motivated by an article by Ian Stewart (Defend the Roman Empire!, Scientific American, Dec.
1999, pp. 136–138), we explore a new strategy of defending the Roman Empire that has the …

A Roman dominating function of a graph G is a labeling f:\,V(G)→{0,1,2\} such that every
vertex with label 0 has a neighbor with label 2. The Roman domination number …

The Roman domination number and Italian domination number (also known as the Roman
{2}-domination number) are graph labeling problems in which each vertex is labeled with …

A Roman dominating function on a graph G is a function f: V (G)→{0, 1, 2} satisfying the
condition that every vertex u for which f (u)= 0 is adjacent to at least one vertex v for which f …

Given real numbers b≥ a> 0, an (a, b)-Roman dominating function of a graph G=(V, E) is a
function f: V→ 0, a, b such that every vertex v with f (v)= 0 has a neighbor u with f (u)= b. An …

In this paper we continue the study of Roman dominating functions in graphs. A signed
Roman dominating function (SRDF) on a graph G=(V, E) is a function f: V→− 1, 1, 2 …

A subset S of the vertex set of a graph G is a dominating set if every vertex of G not in S has
at least one neighbor in S. The domination number γ (G) is defined to be the minimum …

Motivated by articles by Stewart (Defend the Roman Empire!, Sci. Amer.(December 1999)
136–138) and ReVelle and Rosing (Defendens imperium Romanum: A classical problem in …