In this book, we mainly present the recent advance in discrete mathematics. Binding number condition for fractional (g,f,n',m)-critical covered graph and fractional (g,f,n',m)-critical uniform graph are given, characteristics analysis of dendrimers is presented by topological index computing, distance-based indices and polynomials for armchair polyhex nanotubes and nanotori are determined. Furthermore, we study the reverse eccentric connectivity index of haphthylenic lattices.