WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 11, 2012
Hyper Domination in Bipartite Semigraphs
Authors: ,
Abstract: Let $$S$$ be a bipartite semigraph with $$|NX_{a}(y)| ≥ 1$$ for every $$y \in Y$$. A vertex $$ x \in X$$ hyper dominates $$ y \in Y $$ if $$y \in N_{a}(x)$$ or $$y \in N_{a}(N_{Ya}(x)).$$ A subset $$ D subseteq X$$ is called a minimal hyper dominating set of $$S$$ if no proper subset of $$D$$ is a hyper dominating set of $$S$$. The minimum cardinality of a minimal hyper dominating set of $$S$$ is called hyper domination number of $$S$$ and is denoted by $$ γha(S).$$ The concept of hyper independence and hyper irredundant is introduced. Inequalities involving dominating parameters and irredundant parameters are proved.