Multiplicative Zagreb Indices and Extremal Complexity of Line Graphs

‎The number of spanning trees of a graph $G$ is called the complexity of $G$‎. It is known that the complexity of the line graph of a given graph $G$ can‎ be computed as the sum over all spanning trees of $G$ of contributions‎ ‎which depend on various types of products of degrees of vertices of $G$‎. ‎We interpret the contributions in terms of three types of multiplicative‎ Zagreb indices‎, ‎obtaining simple and compact expressions for the complexity of‎ ‎line graphs of graphs with low cyclomatic numbers‎. ‎As an application‎, ‎we‎ determine the unicyclic graphs whose line graphs have the smallest and the‎ largest complexity‎.