MATHEMATICA BOHEMICA, Vol. 129, No. 4, pp. 393-398 (2004)

Signed 2-domination in caterpillars

Bohdan Zelinka

Abstract: 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 $\gamma^2_ s(G)$ and the signed total 2-domination number $\gamma^2_{\rm{st}}(G)$ of a graph $G$ are variants of the signed domination number $\gamma_ s(G)$ and the signed total domination number $\gamma_{\rm{st}}(G)$. Their values for caterpillars are studied.

Keywords: caterpillar, signed 2-domination number, signed total 2-domination number

Classification (MSC2000): 05C69, 05C05

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