Please use this identifier to cite or link to this item:
https://scholarbank.nus.edu.sg/handle/10635/103974
DC Field | Value | |
---|---|---|
dc.title | Products of graphs with their closed-set lattices | |
dc.contributor.author | Koh, K.M. | |
dc.contributor.author | Poh, K.S. | |
dc.date.accessioned | 2014-10-28T02:43:43Z | |
dc.date.available | 2014-10-28T02:43:43Z | |
dc.date.issued | 1988-05 | |
dc.identifier.citation | Koh, K.M.,Poh, K.S. (1988-05). Products of graphs with their closed-set lattices. Discrete Mathematics 69 (3) : 241-251. ScholarBank@NUS Repository. | |
dc.identifier.issn | 0012365X | |
dc.identifier.uri | http://scholarbank.nus.edu.sg/handle/10635/103974 | |
dc.description.abstract | Let L(G), V(G) and Ḡ be, respectively, the closed-set lattice, vertex set, edge set and complement of a graph G. Any lattice isomorphism Φ:L(G){reversed tilde equals}L(G′) induces a bijection Φ:V(G)→V(G′) such that for each x in V(G),Φ(x)=x′ iff Φ({x})={x′}. A graph G is strongly sensitive if for any graph G′ and any lattice isomorphism Φ:L(G){reversed tilde equals}L(G′), the bijection Φ induced by Φ is a graph isomorphism of G onto G′. G is minimally critical if L(G) ∥ L(G-e) for each e in E(G), and maximally critical if L(G) ∥ L(G+e) for any e in E( G ̌). In this paper, we prove that for any two nontrivial graphs G1 and G2, (1) G1 × G2 is maximally critical, and (2) G1 × G2 is strongly sensitive iff G1 × G2 is minimally critical. Necessary and sufficient conditions on G1 such that G1 × G2 is strongly sensitive are also obtained. © 1988. | |
dc.source | Scopus | |
dc.type | Article | |
dc.contributor.department | MATHEMATICS | |
dc.description.sourcetitle | Discrete Mathematics | |
dc.description.volume | 69 | |
dc.description.issue | 3 | |
dc.description.page | 241-251 | |
dc.description.coden | DSMHA | |
dc.identifier.isiut | NOT_IN_WOS | |
Appears in Collections: | Staff Publications |
Show simple item record
Files in This Item:
There are no files associated with this item.
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.