Generalized edge-magic total labellings of models from researching networks

Graph labellings have been used in many applications, such as in the development of redundant arrays of independent disks which incorporate redundancy utilizing erasure codes, some algorithms, design of highly accurate optical gauging systems for use on automatic drilling machines, design of angular synchronization codes, design of optimal component layouts for certain circuit-board geometries, and determining configurations of simple resistor networks which can be used to supply any of a specified set of resistance values. Since some growing graphs were employed successively as models of researching scale-free networks, hierarchical networks and self-similar networks, so we, in this article, will define a new graph labelling and construct network models that admit the new labellings.