Advances and Applications in Discrete Mathematics
Volume 15, Issue 2, Pages 101 - 112
(April 2015) http://dx.doi.org/10.17654/AADMApr2015_101_112 |
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ON MINIMAL DOMINATING SETS FOR SIGNED GRAPHS
P. K. Ashraf and K. A. Germina
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Abstract: A graph with its edges labeled either as positive or negative is called a signed graph. Denoting to be the open neighbourhood of a vertex u, if is a signed graph, a subset of vertices of is a dominating set, if there exists a marking of such that every vertex u of is either in D or whenever and for every A dominating set D of is called a minimal dominating set if no proper subset of D becomes a dominating set. In this paper, we mainly characterize minimal dominating sets for signed graphs along with some other important results on domination for signed graphs. We also discuss briefly on the bounds for the domination number of signed graphs. |
Keywords and phrases: signed graph, domination, dominating set, independent set, irredundant set. |
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