Minimally 4-edge\(^ \#\)-connected graphs
The \(\text{edge}^ \#\)-connectivity of a graph \(G\), defined by \textit{S. B. Maurer} and \textit{P. J. Slater} [Discrete Math. 24, 185-195 (1978; Zbl 0397.05033)], is the minimum cardinality of a cutset \(S\), if one exists, such that \(G-S\) has exactly two components, each containing at least one edge. The paper characterizes some minimally 4-\(\text{edge}^ \#\)- connected graphs, i.e., graphs with \(\text{edge}^ \#\)-connectivity 4, where the deletion of every edge decreases the \(\text{edge}^ \#\)- connectivity.
scientific article; zbMATH DE number 562673
scientific article