Partial cubes and their -graphs
Matjaz Kovse2007, European Journal of Combinatorics
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Abstract
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This paper investigates partial cubes and their associated τ-graphs, extending the characterization of resonance graphs in catacondensed hexagonal graphs. It establishes that every graph is a τ-graph of some median graph, proves the connectivity conditions for τ-graphs, and presents conditions under which median graphs are K_n-free. Key results include the implications of these relationships for mathematical chemistry and the characterization of graphs in relation to certain graph classes. The work concludes with open problems, fostering further research.
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