Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Characterization of $ (r,\,s)$-adjacency graphs of complexes


Authors: Marianne Gardner and Frank Harary
Journal: Proc. Amer. Math. Soc. 83 (1981), 211-214
MSC: Primary 05C75; Secondary 05C65, 05C99
DOI: https://doi.org/10.1090/S0002-9939-1981-0620016-8
MathSciNet review: 620016
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The $ (r,s)$-adjacency graph of a simplicial complex $ K$ has been defined as the graph whose nodes are the $ r$-cells of $ K$ with adjacency whenever there is incidence with a common $ s$-cell. The $ (r,s)$-adjacency graphs for $ r > s$ have been characterized by graph coverings by Dewdney and Harary generalizing the result of Krausz for line-graphs $ (r = 1,s = 0)$. We now complete the characterization by handling the case $ r < s$.


References [Enhancements On Off] (What's this?)

  • [1] J.-C. Bermond, M. C. Heydemann and D. Sotteau, Line graphs of hypergraphs. I, Discrete Math. 18 (1977), 235-241. MR 0463003 (57:2967)
  • [2] J.-C. Bermond, A. Germa and M. C. Heydemann, Graphes représentifs d'hypergraphes, (Colloq. Math. Discretes, Bruxelles, 1978), Cahiers Centre Études Rech. Opér. 20 (1978), 325-329. MR 543175 (80m:05086)
  • [3] A. K. Dewdney and F. Harary, The adjacency graphs of a complex, Czechoslovak Math. J. 26 (1976), 137-144. MR 0427152 (55:188)
  • [4] M. L. Gardner, Forbidden configurations in intersection graphs of $ r$-graphs, Discrete Math. 31 (1980), 85-88. MR 578064 (81g:05086)
  • [5] -, Forbidden configurations of large girth for intersection graphs of hypergraphs, Ars Combinatoria (submitted).
  • [6] B. Grünbaum, Incidence patterns of graphs and complexes, The Many Facets of Graph Theory, Lecture Notes in Math., vol. 110, Springer-Verlag, Berlin and New York, 1968, pp. 115-128. MR 0250920 (40:4152)
  • [7] F. Harary, Graph theory, Addison-Wesley, Reading, Mass., 1969. MR 0256911 (41:1566)
  • [8] M. C. Heydemann and D. Sotteau, Line graphs of hypergraphs. II, Combinatorics, (Colloq. Math. Soc. Janos Bolyai 18), North-Holland, Amsterdam, 1978, pp. 567-582. MR 519291 (80g:05052)
  • [9] D. Krausz, Démonstration nouvelle d'une théorème de Whitney sur les réseaux, Mat. Fiz. Lapok. 50 (1943), 75-89. MR 0018403 (8:284h)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05C75, 05C65, 05C99

Retrieve articles in all journals with MSC: 05C75, 05C65, 05C99


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0620016-8
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society