Paper Info
Title
Perfect Italian domination in trees.
Abstract
A perfect Italian dominating function on a graph G is a function f:V(G)→{0,1,2} satisfying the condition that for every vertex u with f(u)=0, the total weight of f assigned to the neighbors of u is exactly two. The weight of a perfect Italian dominating function is the sum of the weights of the vertices. The perfect Italian domination number of G, denoted γIp(G), is the minimum weight of a perfect Italian dominating function of G. We show that if G is a tree on n≥3 vertices, then γIp(G)≤45n, and for each positive integer n≡0(mod5) there exists a tree of order n for which equality holds in the bound.
Year
DOI
Venue
2019
10.1016/j.dam.2019.01.038
Discrete Applied Mathematics
Keywords
Field
DocType
Italian domination,Roman domination,Roman {2}-domination
Integer,Graph,Discrete mathematics,Combinatorics,Vertex (geometry),Minimum weight,Domination analysis,Mathematics
Journal
Volume
ISSN
Citations 
260
0166-218X
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Teresa W. Haynes177494.22
Michael A. Henning21865246.94