Author:
S. Sunitha ,S. Chandra Kumar
Abstract
An isolated signed total dominating function (ISTDF) of a digraph is a function \(f: V(D) \rightarrow\{-1,+1\}\) such that \(\sum_u \in N-(v) \geq 1\) for every vertex \(v \in V(D)\) and for at least one vertex of \(w \in V(D), f\left(N^{-}(w)\right)=+1\). An isolated signed totaldomination number of \(\mathrm{D}\), denoted by \(\gamma_{\text {ist }}(D)\), in the minimal weight of an isolated signed total dominating function of \(D\). In this paper, we study some properties of ISTDF.
Reference10 articles.
1. Bohdan Zelinka, Liberec, Signed total domination number of a graph, Czechoslovak Mathematical Journal, 51(126)(2001), 2252298 . DOI: https://doi.org/10.1023/A:1013782511179
2. Bohdan Zelinka and Liberec, Signed domination numbers of directed graphs, Czechoslovak Mathematical Journal, $55(130)(2005), 479-482$. DOI: https://doi.org/10.1007/s10587-005-0038-5
3. J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, Elsevier, North Holland, New York, (1986).
4. J.E. Dunbar, S.T. Hedetniemi, M. A. Henning and P. J. Slater, Signed domination in graphs. In: Graph Theory, Combinatorics and Applications. Proc. 7th Internat. Conf. Combinatorics, Graph Theory, Applications, (Y. Alavi, A. J. Schwenk, eds.). John Wiley and Sons, Inc., 1 (1995) 311-322.
5. J. E. Dunbar, S. T. Hedetniemi, M. A. Henning, and A. A. McRae, Minus domination in regular graphs, Discrete Math., 149 (1996), 311-312. DOI: https://doi.org/10.1016/0012-365X(94)00329-H