2019/08/19 by Vaibhav Anu, V., Anu, Aparna Lakshmanan S +1
Computer Science · #05C69 #05C76 #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.1908.06859
openalex publication_date 2019/08/19 · openalex created_date 2019/08/22 · openalex updated_date 2026/07/28
Given a graph G=(V,E), a function f:V→ \0,1,2,3\ having the property that if f(v)=0, then there exist v1,v2∈ N(v) such that f(v1)=f(v2)=2 or there exists w ∈ N(v) such that f(w)=3, and if f(v)=1, then there exists w ∈ N(v) such that f(w)≥ 2 is called a double Roman dominating function (DRDF). The weight of a DRDF f is the sum f(V)=∑v∈ Vf(v). The double Roman domination number, γdR(G), is the minimum among the weights of DRDFs on G. In this paper, we study the impact of some graph operations, such as cartesian product, addition of twins and corona with a graph, on double Roman domination number.