ABSTRACT
It is clear from the content of this and the accompanying book [15] that domination in graphs, along with its many variations, provides an extremely rich area of study. In India, interest in modern domination in graphs was triggered by the monograph-cum-thesis of Walikar [47]. This chapter surveys several topics in the field introduced since then. In particular, the following are discussed: (1) connected domination; (2) strong and weak domination, and domination balance; (3) least domination number; (4) dominating strength and weakness; (5) set and global set domination; (6) point-set and global point-set domination; (7) neighborhood numbers; (8) independent, perfect, and connected neighborhood numbers; (9) domination and neighborhood critical, fixed, free and totally free vertices and edges; and (10) mixed domination. Most proofs are omitted, but a few of the simpler ones are incorporated in order to illustrate the use of some of the concepts.
