Geodesic
Daisy Hamming graphs
Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 2, pp. 421-436

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Daisy graphs of a rooted graph G with the root r were recently introduced as a generalization of daisy cubes, a class of isometric subgraphs of hypercubes. In this paper we first address a problem posed in [A. Taranenko, Daisy cubes: A characterization and a generalization, European J. Combin. 85 (2020) #103058] and characterize rooted graphs G with the root r for which all daisy graphs of G with respect to r are isometric in G, assuming the graph G satisfies the rooted triangle condition. We continue the investigation of daisy graphs G (generated by X) of a Hamming graph ℋ and characterize those daisy graphs generated by X of cardinality 2 that are isometric in ℋ. Finally, we give a characterization of isometric daisy graphs of a Hamming graph K_k_1⋯ K_k_n with respect to 0^n in terms of an expansion procedure.
Keywords: daisy graphs, expansion, isometric subgraphs 
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Dravec, Tanja; Taranenko, Andrej. Daisy Hamming graphs. Discussiones Mathematicae. Graph Theory, Tome 43 (2023) no. 2, pp. 421-436. http://geodesic.mathdoc.fr/item/DMGT_2023_43_2_a6/