Transformations of assembly number for 4-regular graphs

Simple assembly graphs characterize the process of DNA recombination in living cells. The assembly number, number of distinct Hamiltonian sets of polygonal paths, one-sided and middle additivity of a graph are important characteristics of such graphs. This paper investigates transformations of simple assembly graphs that allow one to increase the assembly number or to obtain middle additive graphs. Also the minimum number of loops that must be added to the edges of a tangled chord graph in order to increase its assembly number by 1 is computed.