THE DOMINATION GAME ON SPLIT GRAPHS
Tijo James, Sandi Klavžar, Ambat Vijayakumar · Bulletin of the Australian Mathematical Society · 2018
We investigate the domination game and the game domination number $\unicode[STIX]{x1D6FE}_{g}$ in the class of split graphs. We prove that $\unicode[STIX]{x1D6FE}_{g}(G)\leq n/2$ for any isolate-free $n$ -vertex split graph $G$ , thus strengthening the conjectured $3n/5$ general bound and supporting Rall’s $\lceil n/2\rceil$ -conjecture. We also characterise split graphs of even order with $\unicode[STIX]{x1D6FE}_{g}(G)=n/2$ .