Abstract
The multiplicative first Zagreb index of a graph H is defined as the product of the squares of the degrees of vertices of H. The line graph of a graph H is denoted by L(H) and is defined as the graph whose vertex set is the edge set of H where two vertices of L(H) are adjacent if and only if they are adjacent in H. The multiplicative first Zagreb index of the line graph of a graph H is referred to as the reformulated multiplicative first Zagreb index of H. This paper gives characterization of the unique graph attaining the minimum or maximum value of the reformulated multiplicative first Zagreb index in the class of all (i) trees of a fixed order (ii) connected unicyclic graphs of a fixed order.