<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e117" altimg="si8.svg"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>-conjectures on the domination game and claw-free graphs

Let γg(G) be the game domination number of a graph G. Rall conjectured that if G is traceable graph, then γg(G)≤12n(G). Our main result verifies conjecture over class line graphs. Moreover, in this paper we put forward δ(G)≥2, We show both conjectures hold true for claw-free cubic further prove upper bound γg(G)≤1120n(G) graphs minimum degree at least 2. Computer experiments supporting new and sharpness examples are also presented.