The domination game played on diameter 2 graphs

Bujtás, Csilla and Irsic, Vesna and Klavzar, Sandi and Xu, Kexiang (2021) The domination game played on diameter 2 graphs. AEQUATIONES MATHEMATICAE, Publis. ISSN 0001-9054

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Abstract

Let gamma(g)(G) be the game domination number of a graph G. It is proved that if diam(G) = 2, then gamma(g)(G) <= inverted right perpendicularn(G)/2inverted left perpendicular - left perpendicularn(G)/11right perpendicular. The bound is attained: if diam(G) = 2 and n(G) <= 10, then gamma(g)(G) = inverted right perpendicularn(G)/2inverted left perpendicular if and only if G is one of seven sporadic graphs with n(G) = 6 or the Petersen graph, and there are exactly ten graphs of diameter 2 and order 11 that attain the bound.

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