Labellings and invariants of models from complex networks

Graph labelings related with communication networks have been extensively investigated because their applications to real problems. Some results on graph labellings are obtained here. Scale-free graphs are coming from scale-free networks a few years ago. We use spanning trees to study some important characteristics of scale-free networks, and obtain some results related with scale-free networks. Furthermore, we provide some connections between invariants of graphs in order to apply graph-theoretical methods to network problems.