摘要： A configuration of the lit-only σ -game on a graph Γ is an assignment of one of two states, on or off , to each vertex of Γ . Given a configuration, a move of the lit-only σ -game on Γ allows the player to choose an on vertex s of Γ and change the states of all neighbors of s . Given an integer k , the underlying graph Γ is said to be k -lit if for any configuration, the number of on vertices can be reduced to at most k by a finite sequence of moves. We give a description of the orbits of the lit-only σ -game on nondegenerate graphs Γ which are not line graphs. We show that these graphs Γ are 2-lit and provide a linear algebraic criterion for Γ to be 1-lit. 其他題名： J Algebr Comb 出版者： Boston: Springer US 出版日期： 2015-03-01 出處： Journal of algebraic combinatorics, 2015-03, Vol.41 (2), p.385-395 資源來源： Springer Nature OA Free Journals 版權： The Author(s) 2014 識別號： ISSN: 0925-9899 識別號： ISSN: 1572-9192 識別號： EISSN: 1572-9192 識別號： DOI: 10.1007/s10801-014-0540-7
