Indicated total domination game
Michael A. Henning, Douglas F. Rall

TL;DR
This paper introduces the indicated total domination game on graphs, analyzing the strategic interactions between players and establishing bounds on the game’s outcome related to existing domination parameters.
Contribution
It defines the indicated total domination game, explores its properties, and proves bounds relating it to the upper total domination number.
Findings
The indicated total domination number is bounded below by the upper total domination number.
Optimal strategies for both players are characterized.
The paper establishes fundamental bounds and properties of the game.
Abstract
A vertex in a graph totally dominates a vertex if is adjacent to in . A total dominating set of is a set of vertices of such that every vertex of is totally dominated by a vertex in . The indicated total domination game is played on a graph by two players, Dominator and Staller, who take turns making a move. In each of his moves, Dominator indicates a vertex of the graph that has not been totally dominated in the previous moves, and Staller chooses (or selects) any vertex adjacent to that has not yet been played, and adds it to a set that is being built during the game. The game ends when every vertex is totally dominated, that is, when is a total dominating set of . The goal of Dominator is to minimize the size of , while Staller wants just the opposite. Providing that both players are playing optimally with respect to…
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Taxonomy
TopicsAdvanced Graph Theory Research
