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caterpillar; signed 2-domination number; signed total 2-domination number
A caterpillar is a tree with the property that after deleting all its vertices of degree 1 a simple path is obtained. The signed 2-domination number $\gamma ^2_{\mathrm s}(G)$ and the signed total 2-domination number $\gamma ^2_{\mathrm {st}}(G)$ of a graph $G$ are variants of the signed domination number $\gamma _{\mathrm s}(G)$ and the signed total domination number $\gamma _{\mathrm {st}}(G)$. Their values for caterpillars are studied.
[1] A. Recski: Maximal results and polynomial algorithms in VLSI routing. Combinatorics, Graphs, Complexity. Proc. Symp. Prachatice, 1990. JČMF Praha, 1990.
[2] T. W. Haynes, S. T. Hedetniemi, P. J. Slater: Fundamentals of Domination in Graphs. Marcel Dekker, New York, 1998. MR 1605684
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