Solvable join of graphs - Gervacio, Severino V. (Animo Repository, 2006)
Initially, assign the state O or 1 to each vertex of a graph G. For each vertex v of G, let the move [v] mean switch the state of vertex v and each vertex adjacent to v. If there is a sequence of moves that brings the graph G to the 0-state (all vertices have O state) we say that the given initial state is solvable. If all initial states of a graph are solvable, we call the graph a solvable graph. We investigate the solvability of the join of two graphs.