On the Assignment Graphs of Oriented Graphs
Jared Glassband, Garrison Koch, Sophia Lebiere, Xufei Liu, and Evan, Sabini
TL;DR
This paper extends graph pebbling concepts to oriented graphs, classifies graphs with fully traversable pebbling assignments, and explores cases where non-fully traversable assignments are isomorphic to their assignment graphs.
Contribution
It introduces a classification for graphs with fully traversable pebbling assignments and explores isomorphisms in non-fully traversable cases.
Findings
Classification of graphs with fully traversable pebbling assignments
Identification of cases with non-fully traversable assignments isomorphic to their assignment graphs
Extension of graph pebbling theory to oriented graphs
Abstract
In this paper, we extend the ideas of graph pebbling to oriented graphs and find a classification for all graphs with fully traversable pebbling assignments that are isomorphic to their assignment graph. We then give some cases in which a graph with a non-fully traversable pebbling assignment is isomorphic to its assignment graph.
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Taxonomy
TopicsArtificial Intelligence in Games · Advanced Graph Theory Research · Computational Geometry and Mesh Generation