Pendant Total Domination Polynomial of Some Families of Standard Graphs - Rani, Jyoti; Mehra, Seema (Communications in Mathematics and Applications, 2023)
In this article, our aim is to determine the pendant total domination polynomial of some families of standard graphs and obtain some properties of coefficients and nullity of the pendant total domination polynomial of a connected graph \(G\). Consider \(G\) as a simple connected graph and its vertex and edge sets are defined as \(V_\) and \(E_\), respectively. A set \(T V_\) is said to be a total dominating set of graph \(G\) if all the vertices of the graph must attached with some vertex of \(T \). A set \(T V_\) is said to be a PTDS if \(T\) is a TDS and \(T \) contains at least a single pendant vertex.