New classes of magic and anti-magic total labelings for directed graphs are defined. Star Labelings assign to each vertex v the weight w(v) which equals the sum of labels assigned to v and to all arcs incident to v. Star-Complete Labelings assign to each vertex the weight which equals the sum of labels assigned to v, to all arcs incident to v, and to vertices in the in-neighborhood of v. In-ore magic and in-arc antimagic labelings are defined by assigning a weight w(u̅v) to each arc u̅v which equals the sum of labels on arc u̅v and the vertex v to which it is incident. Properties and examples of star, star-complete, and in-arc magic and anti-magic digraphs are explored.
International Conference on Mathematics and Computer Science 2010 (ICMCS 2010). Proceedings of the International Conference on Mathematics and Computer Science (Chennai, India 5-6 February, 2010)