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101.
Simpozij o nodusih v ščitnici : elektronski zbornik znanstvenih prispevkov
2025, proceedings of peer-reviewed scientific conference contributions (domestic conferences)

Published in DiRROS: 03.03.2025; Views: 81; Downloads: 24
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Resonance graphs of plane bipartite graphs as daisy cubes
Simon Brezovnik, Zhongyuan Che, Niko Tratnik, Petra Žigert Pleteršek, 2025, original scientific article

Abstract: We characterize plane bipartite graphs whose resonance graphs are daisy cubes, and therefore generalize related results on resonance graphs of benzenoid graphs, catacondensed even ring systems, as well as $2$-connected outerplane bipartite graphs. Firstly, we prove that if $G$ is a plane elementary bipartite graph other than $K_2$, then the resonance graph of $G$ is a daisy cube if and only if the Fries number of $G$ equals the number of finite faces of $G$. Next, we extend the above characterization from plane elementary bipartite graphs to plane bipartite graphs and show that the resonance graph of a plane bipartite graph $G$ is a daisy cube if and only if $G$ is weakly elementary bipartite such that each of its elementary component $G_i$ other than $K_2$ holds the property that the Fries number of $G_i$ equals the number of finite faces of $G_i$. Along the way, we provide a structural characterization for a plane elementary bipartite graph whose resonance graph is a daisy cube, and show that a Cartesian product graph is a daisy cube if and only if all of its nontrivial factors are daisy cubes.
Keywords: daisy cube, fries number, peripherally 2-colorable, plane (weakly) elementary bipartite graph, resonance graph
Published in DiRROS: 03.03.2025; Views: 63; Downloads: 34
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