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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Mphako-Banda, Eunice
School of Mathematics University of the Witwatersrand
Electrical & Electronics Engineering

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The mincut graph of a graph Kriel, Christo; Mphako-Banda, Eunice
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 1 (2026): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2026.14.1.3

Abstract

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 "Graph Dynamics". Thus we ask and attempt to answer questions such as 'Which graphs appear as images of graphs?'; 'Which graphs are fixed under the operator?'; 'What happens if the operator is iterated?' We show that every graph is a minimum cut-set graph, henceforth called a mincut graph, of infinite depth and with an infinite number of roots.
Co-Authors Kriel, Christo