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Proceedings of the American Mathematical Society
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
MathSciNet review: 620016
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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$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0620016-8
PII: S 0002-9939(1981)0620016-8
Article copyright: © Copyright 1981 American Mathematical Society