First Zagreb Index and its Characteristics on Neutrosophic Graph

Topological indices mark an irreplaceable place for applications in crisp and fuzzy graphs. These indices are extended to the neutrosophic graphical idea to rectify the imprecise values or information acquired before, since the uncertain cases are organized and allocated as a separate membership called "indeterminacy". We apply and explore the First zagreb index and its properties on the neutrosophic graphical system in the line of Wiener and Forgotten indices. This fills the gap between fuzzy and its graphical extensions on indices discussion, thereby extends the applicable areas. Also, an improvised and unique application is portrayed to observe the importance of First zagreb index in the neutrosophic theme of graphs. This contributes to the real life in a greater way than the fuzzy idea.