The diversity of domination

✍ Scribed by Michael A. Henning; Ortrud R. Oellermann; Henda C. Swart

• Book ID: 103061406
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 706 KB
• Volume: 161
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(95)00074-7

✦ Synopsis

For any graph G and a set ~ of graphs, two distinct vertices of G are said to be ~adjacent if they are contained in a subgraph of G which is isomorphic to a member of ~. A set S of vertices of G is an ~-dominating set (total ~¢~-dominating set) of G if every vertex in V(G)-S (V(G), respectively) is 9¢g-adjacent to a vertex in S. An ~-dominating set of G in which no two vertices are oCf-adjacent in G is an ~,~-independent dominating set of G. The minimum cardinality of an ~-dominating set, total ~-dominating set and ~-independent dominating set of G is known as the ~-domination number, total ~-domination number, and ~Yf-independent dominating number, of G, denoted, respectively, by 7ae(G),7~(G), and i~e(G).

We survey the applications and bounds obtained for the above domination parameters if ~={K,} or Jf = {Pil2 ~< i ~< n}, for an integer n >/2.