Recognizable Languages of k-Forcing Automata

In this study, we show that automata theory is also a suitable tool for analyzing a more complex type of the k-forcing process. First, the definition of k-forcing automata is presented according to the definition of k-forcing for graphs. Moreover, we study and discuss the language of k-forcing automata for particular graphs. Also, for some graphs with different k-forcing sets, we study the languages of their k-forcing automata. In addition, for some given recognizable languages, we study the structure of graphs. After that, we show that k-forcing automata arising from isomorph graphs are also isomorph. Also, we present the style of words that can be recognized with k-forcing automata. Moreover, we introduce the structure of graphs the k-forcing automata arising from which recognize some particular languages. To clarify the notions and the results obtained in this study, some examples are submitted as well.