Abstract：The edge-magic total labelling of a graph G (p， q) means that the sum of labellings of any edge and its incident vertice is equal to a constant ， and the mapping of all labelling values of vertice and edges is the set . In this paper， a judge algorithm is designed to get all edge-magic total labelling of bicyclic graphs within 15 vertices. Through the analysis of the results， finding the rules of edge-magic total labelling for two kinds of bicyclic graphs， and defining the new graph operational symbols CnΔClSymbolQCpSm and CnΔClΔSm to describe such graphs， several theorems are summarized and proved finally. It is further conjectured that the relevant conclusions are still valid when the vertex p≥16.
2020, Vol. 54 
