2,160 research outputs found
Minimum Light Numbers in the -Game and Lit-Only -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 let be the minimum integer such that given any starting configuration of there must exist a sequence of valid moves which takes to a configuration with at most ON vertices provided there is a sequence of regular moves which brings to a configuration in which there are ON vertices. The shadow graph of a graph is obtained from by deleting all loops. We prove that if is unicyclic and give an example to show that the bound is tight. We also prove that if is a two-dimensional grid graph and if is a two-dimensional grid graph but not a path and
Spartan Daily, October 24, 2005
Volume 125, Issue 33https://scholarworks.sjsu.edu/spartandaily/10176/thumbnail.jp
Spartan Daily, September 8, 1986
Volume 87, Issue 7https://scholarworks.sjsu.edu/spartandaily/7464/thumbnail.jp
The Montana Kaimin, November 4, 1932
Student newspaper of the University of Montana, Missoula.https://scholarworks.umt.edu/studentnewspaper/2442/thumbnail.jp
The Montana Kaimin, November 2, 1939
Student newspaper of the University of Montana, Missoula.https://scholarworks.umt.edu/studentnewspaper/10886/thumbnail.jp
Spartan Daily, May 25, 1939
Volume 27, Issue 144https://scholarworks.sjsu.edu/spartandaily/2934/thumbnail.jp
The Montana Kaimin, November 1, 1932
Student newspaper of the University of Montana, Missoula.https://scholarworks.umt.edu/studentnewspaper/2441/thumbnail.jp
Spartan Daily, February 20, 1959
Volume 46, Issue 75https://scholarworks.sjsu.edu/spartandaily/3854/thumbnail.jp
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