On the Strong Circuit Uniqueness and its Application to the Circuit Characterization of Graphs

Abstract

On the basis of circuit uniqueness, the concept of strong circuit uniqueness is introduced, and some graphs with the property of strong circuit uniqueness are identified. The results are then used to prove successfully the circuit uniqueness of the graphs $K_m\cup K_n$ and $K_{m,n}$. This represents an improvement on the previous papers on the same subject.