Characterization of (𝑟,𝑠)-adjacency graphs of complexes
Marianne L. Gardner, Frank Harary · Proceedings of the American Mathematical Society · 1981
The ( r , s ) (r,s) -adjacency graph of a simplicial complex K K has been defined as the graph whose nodes are the r r -cells of K K with adjacency whenever there is incidence with a common s s -cell. The ( r , s ) (r,s) -adjacency graphs for r > s r > s have been characterized by graph coverings by Dewdney and Harary generalizing the result of Krausz for line-graphs ( r = 1 , s = 0 ) (r = 1,s = 0) . We now complete the characterization by handling the case r > s r > s .