A Study of disjunctive total domination in claw-free graphs

• Main Authors: Sheng-Fu Wu, 吳升福
• Other Authors: Sheng-Lung Peng
• Format: Others
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/60889029005038313770

碩士 === 國立東華大學 === 資訊工程學系 === 103 === Total dominating set is a subset D of V for a graph G = (V;E) such that every vertex is adjacent to at least one member of D. Total dominating number of a graph G, denoted by t(G), is the size of a minimum total dominating set of G. Disjunctive total dominating set is a subset D of V for a graph G = (V;E) such that every vertex of G is adjacent to at least one member of D or there are two vertices of distance 2 in D. Disjunctive total dominating number of a graph G, denoted by dt (G), is the size of a minimum disjunctive total dominating set of vertices in G. By the denition, dt(G)<t(G). A claw-free graph is a graph that does not contain K1;3 as an induced subgraph. It is known that if G is a claw-free graph of order n with minimum degree two, then t(G) (n+2)=2. In this thesis, we show that if G is a connected claw-free graph of order n with minimum degree two, then dt (G) <=2n/5+ 2.