Characteristics of winnable games of ELLO.

Abstract

This manuscript presents some proofs of prepositions, corollaries, and a theorem, that provide some illustrations of winnable games of Elimination Lit-Lights Out (ELLO). This game is played on 2-colored graph, i.e. red and green, by choosing one by one vertices on the graph. A linear ordering of vertices on a graph is called strategy. The objective of the game is to eliminate all vertices on the graph. There are two prepositions, three corollaries and one theorem to be considered. Characteristics of a strategy that can win a given ELLO game are given in the first preposition. The second preposition discusses properties of a game that satisfy parity condition but can not be won. The first corollary discusses the relationship between strategy and winnable game. The second corollary gives characteristics of winnable game on a complete graph. The third corollary discusses the strategy and the reverse order of the strategy. The theorem on this manuscript states that winnable game will satisfy parity condition.