The domination game played on diameter 2 graphs

2020/09/21 by Csilla Bujtás, Bujtás, Csilla, Vesna Iršič +5 · 1 citation
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.09760

openalex publication_date 2020/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let γ_g(G) be the game domination number of a graph G. It is proved that if \rm diam(G) = 2, then γ_g(G) ≤ \lceil (n(G))/(2) \rceil- \lfloor (n(G))/(11)\rfloor. The bound is attained: if \rm diam(G) = 2 and n(G) ≤ 10, then γ_g(G) = \lceil (n(G))/(2) \rceil 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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• 1/2-conjectures on the domination game and claw-free graphs

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