منابع مشابه
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-...
متن کاملMinimum Light Numbers in the σ-Game and Lit-Only σ-Game on Unicyclic and Grid Graphs
Consider a graph each of whose vertices is either in the ON state or in the OFF state and call the resulting ordered bipartition into ON vertices and OFF vertices a configuration of the graph. A regular move at a vertex changes the states of the neighbors of that vertex and hence sends the current configuration to another one. A valid move is a regular move at an ON vertex. For any graph G, let...
متن کاملLit-only sigma game on a line graph
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 ...
متن کامل2 00 9 Difference between minimum light numbers of sigma - game and lit - only sigma - game ∗
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. The following result is proved in this note: given any starting configuration x of a tree, if there is a sequence of regular moves which brings x to another configuration ...
متن کاملOn for S Cal Lit
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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