Year: 2025
Type: article
Abstract: A simple connected graph is strongly connected if there exists a directed path between every pair of vertices in both directions. Robbins showed that every \(2\)-edge-connected graph can be given edge orientations that result in the graph being strongly connected. But a random assignment of edge directions may or may not result in a graph being strongly connected. We say that a \(2\)-edge-connected graph is very strongly connected if any choice of edge orientations that does not feature a vertex having maximal or minimal indegree yields a strongly connected graph. We classify all graphs as either very strongly connected or not very strongly connected.
DOI: 10.63151/amjc.v4i.36
Authors: Madison Cox, Kaylee Freudenthal, Hannah Golab, Ruth Perry, Jeff Rushall
Institution: Northern Arizona University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4413637504