Siva Reddy, P., Prashanth, B. (2012). The common minimal dominating signed graph. Transactions on Combinatorics, 1(3), 39-46. doi: 10.22108/toc.2012.1896

P. Siva Reddy; B. Prashanth. "The common minimal dominating signed graph". Transactions on Combinatorics, 1, 3, 2012, 39-46. doi: 10.22108/toc.2012.1896

Siva Reddy, P., Prashanth, B. (2012). 'The common minimal dominating signed graph', Transactions on Combinatorics, 1(3), pp. 39-46. doi: 10.22108/toc.2012.1896

Siva Reddy, P., Prashanth, B. The common minimal dominating signed graph. Transactions on Combinatorics, 2012; 1(3): 39-46. doi: 10.22108/toc.2012.1896

^{}Dept. of Mathematics, Acharya Institute of Technology, Bangalore-560 090, India

Abstract

In this paper, we define the common minimal dominating signed graph of a given signed graph and offer a structural characterization of common minimal dominating signed graphs. In the sequel, we also obtained switching equivalence characterizations: $\overline{S} \sim CMD(S)$ and $CMD(S) \sim N(S)$, where $\overline{S}$, $CMD(S)$ and $N(S)$ are complementary signed graph, common minimal signed graph and neighborhood signed graph of $S$ respectively.

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