A Short Survey on the Disjunctive (Total) Domination Numbers of Graphs

This survey reviews recent results on the disjunctive domination numbers and the disjunctive total domination numbers in graphs. Tight bounds and exact values are presented for trees, grids, and Harary graphs. The ratio [Formula: see text] is analyzed for various graph families, where [Formula: see text] and [Formula: see text] are the domination number and the disjunctive domination number of a graph [Formula: see text]. Algorithmic results, including NP-completeness and polynomial-time solutions for trees and interval graphs, are discussed. The survey concludes with open problems, such as the cubic graph conjecture and the claw-free graph conjecture.