A note on total domination

✍ Scribed by Robert B Allan; Renu Laskar; Stephen Hedetniemi

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 278 KB
• Volume: 49
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(84)90145-6

✦ Synopsis

For a graph G, let ~'(G), 3,z(G), i(G) and ir(G) denote the domination, total domination, independent domination and irredundance numbers of G, respectively. The following conjectures due to Robyn Dawes are proved:
G)<~p and (ii) i(G)+ ~/z(G)~2. It is also shown that (iii) 3,t(G) ~<2ir(G) and (iv) 3'(G) ~< 2ir(G) -(k + 1). where k is the maximum number of isolates in an Jr(G) set. This last result improves the result, obtained independently by Boll6bas and Cockayne [6], Allan and Laskar [2].