4 research outputs found
The domination game played on diameter 2 graphs
Let be the game domination number of a graph . It is proved
that if , then . The bound is
attained: if and , then if and only if is one of seven
sporadic graphs with or the Petersen graph, and there are exactly
ten graphs of diameter and order that attain the bound
The domination game played on diameter 2 graphs
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