Truth-teller and liar puzzles and their graphs

In this paper we present some type of truth-tellers and liars puzzles, especially SS, SW amd SW-L types. We make the graphs of these puzzles. The graph of a puzzle has all information about the puzzle in case of clear puzzles. We show that there is no clear SS-type puzzle with unique solution. We give an algorithm, which can provide all possible solutions of a clear SS-type puzzle. In case of non-clear puzzles, we must choose among these possible solutions, as we show in some examples. After this we examine the SW-type puzzles, and we give an algorithm based on local information using the graph of the puzzle which is very helpful to solve this puzzle. After this we show a special example, when this graph-algorithm does not work alone. This example is an SW-L-type puzzle. Finally we show a graph-algorithm, which is based on global information, and it can solve the SW-L-type puzzles.