Total Domination in Graphs: New Perspectives and Results

In this research paper, we initiate a study of such questions in the present context of total domination theory within graph theory from new perspectives and results concerned with formal definitions, mathematical formulations, theorems and practical applications. Description Total domination is a tool used to determine the graph that has minimum number of vertices can monitor or control all other vertices - factors of interest for problems related, amongst others fields as network optimization and resilience analysis. This paper covers fundamental definitions as well their most recent theoretical bounds, algorithmic complexities and practical examples arising in applications from the real world. The obtained results could be helpful in deciphering, exploiting and administering the concept of total domination further.