Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6871827 | Discrete Applied Mathematics | 2016 | 7 Pages |
Abstract
For a graph G=(V,E), a double Roman dominating function is a function f:Vâ{0,1,2,3} having the property that if f(v)=0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor with f(w)=3, and if f(v)=1, then vertex v must have at least one neighbor with f(w)â¥2. The weight of a double Roman dominating function f is the sum f(V)=âvâVf(v), and the minimum weight of a double Roman dominating function on G is the double Roman domination number of G. We initiate the study of double Roman domination and show its relationship to both domination and Roman domination. Finally, we present an upper bound on the double Roman domination number of a connected graph G in terms of the order of G and characterize the graphs attaining this bound.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Robert A. Beeler, Teresa W. Haynes, Stephen T. Hedetniemi,