Domination Number on Balanced Signed Graphs
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R. Malathi and A. Alwin investigate the concept of domination number on balanced signed graphs. They define a signed graph as an ordinary graph where each edge is marked as positive or negative, and is balanced if each cycle contains an even number of negative edges. The paper finds domination sets on the vertices of bipartite graphs and shows that changing the signs of d edges can convert a signed graph G into a balanced graph. It also investigates the number D(F) as the largest d(G) where G is a signed graph based on F. The paper concludes that if F is a complete bipartite graph with t vertices in each part, then D(F) is at most 1/2t^2 -
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Domination Number on Balanced Signed Graphs
- 1. International Journal of Computing Algorithm, Vol 3(3), June 2014 ISSN(Print):2278-2397 Website: www.ijcoa.com Domination Number on Balanced Signed Graphs R.Malathi1 , A.Alwin2 1 Asst.Prof, 2 M.Phil Scholar Dept of Mathematics, Scsvmv Univeristy, Enathur, Kanchipuram, Tamil Nadu E-mail: malathihema@yahoo.co.in, alwin.best111@gmail.com Abstract A signed graph based on F is an ordinary graph F with each edge marked as positive or negative. Such a graph is called balanced if each of its cycles includes an even number of negative edges. We find the domination set on the vertices, on bipartite graphs and show that graphs has domination Number on signed graphs, such that a signed graph G may be converted into a balanced graph by changing the signs of d edges. We investigate the number D (F) defined as the largest d (G) such that G is a signed graph based on F. If F is the complete bipartite graph with t vertices in each part, then D(f)≤ ½ t² -ct for some positive constant c.