omination in bipartite graphs

eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences April 2010 22 1 89 94 jusps-A 1032 article omination in bipartite graphs V. Swaminathan (sulanesri@yahoo.com) 1 Y.B. Venkatakrishnan (venkatakrish2@maths.sastra.edu) 2 Reader (Retd.) S.N. College, Madurai - 625 002 (INDIA) Department of Mathematics, Tanjor - 613 402 (INDIA) Let G= (X,Y,E,) be a bipartite graph. A subset D of X is an X-dominating set if every x € X-D is X-adjacent to at least one vertex  u€ D The cardinality of a minimum X-dominating set is called the X-domination number and is denoted by Yx (G) . A minimum cardinality subset  S X which dominates all vertices in Y, such a set is called Y-dominating set. The Y-domination number is denoted by Yy (G) We characterize graphs for which Yy (G) = Yy (G) , Yy (G) = Yy (G) , Yhr (G) = I and also prove Yy (G) ≤ Yx (G)  https://www.ultrascientist.org/paper/1032/ Bipartite graphs X-dominating sets Y-dominating sets Hyper Y-dominating sets.