Two-lit trees for lit-only σ-game

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Lit-only sigma-game on pseudo-trees

A configuration of a graph is an assignment of one of two states, ON or OFF, to each vertex of it. A regular move at a vertex changes the states of the neighbors of that vertex. A valid move is a regular move at an ON vertex. A pseudo-tree is a graph obtained from a tree by attaching zero or more loops. The following result is proved in this note: given any starting configuration x of a pseudo-...

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Let Γ be a connected graph. For any x ∈ F (Γ) 2 , a move of the litonly sigma game consists of choosing some v ∈ V (Γ) with x(v) = 1 and changing the values of x at all those neighbors of v. An orbit is a maximal subset of F (Γ) 2 any two of which can reach each other by a series of moves. The minimum light number of Γ is maxK minx∈K #supp(x), where K runs through all orbits. The subspace of F ...

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ژورنال

عنوان ژورنال: Linear Algebra and its Applications

سال: 2013

ISSN: 0024-3795

DOI: 10.1016/j.laa.2012.08.033