"Graphs with Large Italian Domination Number" by Teresa W. Haynes, Michael A. Henning et al.
 

Graphs with Large Italian Domination Number

Document Type

Article

Publication Date

11-1-2020

Description

An Italian dominating function on a graph G with vertex set V(G) is a function f: V(G) → { 0 , 1 , 2 } having the property that for every vertex v with f(v) = 0 , at least two neighbors of v are assigned 1 under f or at least one neighbor of v is assigned 2 under f. The weight of an Italian dominating function f is the sum of the values assigned to all the vertices under f. The Italian domination number of G, denoted by γI(G) , is the minimum weight of an Italian dominating of G. It is known that if G is a connected graph of order n≥ 3 , then γI(G)≤34n. Further, if G has minimum degree at least 2, then γI(G)≤23n. In this paper, we characterize the connected graphs achieving equality in these bounds. In addition, we prove Nordhaus–Gaddum inequalities for the Italian domination number.

Plum Print visual indicator of research metrics
PlumX Metrics
  • Citations
    • Citation Indexes: 11
  • Usage
    • Abstract Views: 3
  • Captures
    • Readers: 3
see details

Share

COinS