Total Domination Polynomials: A New Approach

Graph theory is one of the most relevant and fastest growing branches of mathematics. Owing to its exponential growth in the past few decades and its extensive applications in diverse fields, Graph theory has become the foundation stone of applied mathematics. The book successfully employs vertex cover polynomials to determine the total domination polynomials of some graphs. It is known that the problem of finding total dominating sets in simple graphs can be translated to the concept of vertex covers in hypergraphs. This prompted us to study total domination polynomials using vertex cover polynomials in hypergraphs.