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West, Douglas B. Stodolsky, Burak Yildiran 2015-09-28T15:20:09Z 2015-09-28T15:20:09Z 10000-01-01 2008 2008 Given a partition pi of V (G) with parts ( V1, V2, ... , V t). A pi-dominating set B is a dominating set that is the union of parts of pi. The pi-domination number gamma(G,pi) of G is the size of a smallest pi-dominating set. If each Vi in pi has size at most 2, we call pi a coupling of G and say that the vertices in Vi are coupled together. The coupled domination number, gamma cpl(G), is the maximum of gamma(G,pi) over all couplings pi of G. We also study coupled domination in trees. This topic was introduced by Slater and Seo, who established the coupled domination number of several different kinds of trees. They obtained a tree T' with gammacpl( T') = 8 and gamma(T' ) = 5. We show that gcplT gT ≥8/5 for every tree T with at least 2 vertices. Made available in DSpace on 2015-09-28T15:20:09Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3337932.pdf: 3521023 bytes, checksum: f2499da093fb6b7ed2927e668f4eaa1a (MD5) Previous issue date: 2008 Embargo set by: Seth Robbins for item 88197 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 69 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008. http://hdl.handle.net/2142/86916 (MiAaPQ)AAI3337932 eng Mathematics Domination in Sparse Graphs text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.