The mincut graph of a graph - Christo Kriel; Eunice Mphako-Banda (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2026)
In this paper we introduce an intersection graph of a graph G, with vertex set the minimum edge-cuts of G. We find the minimum cut-set graphs of some well-known families of graphs and study the mincut graph as a graph operator. In doing so we follow the research programme on graph operators, as introduced by Prisner in the 1995 monograph