Double domination in signed graphs

• Main Authors: P.K. Ashraf, K.A. Germina
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2016-12-01
• Series: Cogent Mathematics
• Subjects: signed graph; domination; double domination
• Online Access: http://dx.doi.org/10.1080/23311835.2016.1186135

A graph with either positive or negative labels on the edge becomes a signed graph. Given a signed graph $ \Sigma =(V,E,\sigma ) $, a subset D of V is said to be a double dominating set for $ \Sigma $, if it satisfies the following conditions: (i) every vertex u of $ \Sigma $ is either in D and u has at least one neighbour in D or whenever $ u\in V\setminus D $, $ |N(u)\cap D| \ge 2 $ (ii) $ \Sigma [D:V \setminus D] $ is balanced where N(u) denotes the open neighbourhood of a vertex u and $ \Sigma [D:V \setminus D] $ is the subgraph of the $ \Sigma $ induced by the edges between the vertices in D and $ V\setminus D $. In this paper, we initiate the discussion on the double domination in signed graphs.