Burosch, Gustav; Havel, Ivan; Laborde, Jean-Marie Distance monotone graphs and a new characterization of hypercubes. (English) Zbl 0768.05033 Discrete Math. 110, No. 1-3, 9-16 (1992). Summary: The aim of this paper is to study the class of s.c. distance monotone graphs which arise naturally when investigating some intersection properties of graphs. A new characterization of hypercubes is also obtained. Cited in 5 Documents MSC: 05C12 Distance in graphs 05C75 Structural characterization of families of graphs 05C65 Hypergraphs Keywords:distance monotone graphs; intersection properties; hypercubes PDFBibTeX XMLCite \textit{G. Burosch} et al., Discrete Math. 110, No. 1--3, 9--16 (1992; Zbl 0768.05033) Full Text: DOI References: [1] Bandelt, H.-J.; Mulder, H. M., Infinite median graphs (0,2)-graphs, and hypercubes, J. Graph Theory, 7, 487-497 (1983) · Zbl 0525.05055 [2] Berman, A.; Kotzig, A., Bipartite graphs with a central symmetry and (1,−1)-matrices, Ann. Discrete Math., 8, 37-42 (1980) · Zbl 0446.05025 [3] Mulder, H. M., The interval function of a graph (1980), Mathematisch Centrum: Mathematisch Centrum Amsterdam · Zbl 0446.05039 [4] Burosch, G.; Laborde, J.-M., Some intersection theorems for structures, European J. Combin., 9, 207-214 (1988) · Zbl 0679.05060 [5] Havel, I.; Laborde, J.-M., On distance monotone graphs, (Colloquia Mathematica Societatis János Bolyai, 52 (1987), Combinatorics: Combinatorics Eger, (Hungary)), 557-561 · Zbl 0721.05016 [6] Laborde, J.-M., Caractérisation locale du graphe du \(n\)-cube, (Benzaken, C., Algègre Appliquée et Combinatoire (1978)), 198-200, Grenoble · Zbl 0404.05054 [7] Nes̆etr̆il, J., Teorie grafŮ, SNTL (1979), Praha This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.