multiplicative zagreb indices and extremal complexity of line graphs

The number of spanning trees of a graph g is called thecomplexity of g. it is known that the complexity of the linegraph of a given graph g can be computed as the sum over allspanning trees of g of contributions which depend on varioustypes of products of degrees of vertices of g. we interpret thecontributions in terms of three types of multiplicative zagrebindices, obtaining simple and compact expressions for the complexityof line graphs of graphs with low cyclomatic numbers.as an application, we determine the unicyclic graphs whose linegraphs have the smallest and the largest complexity.