| Domination Parameters and Vertex-Contraction-Critical Graphs |
| Received:January 05, 2004 |
| Key Words:
vertex-contraction domination number upper domination number independent domination number independence number.
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| Abstract: |
| Let $G$ be a simple graph and $u,v\in V(G)$. The graph $G_{uv}$ is called the vertex-contraction of $G$, if we identify the vertices $u$ and $v$ and remove all resulting loops and duplicate edges. This paper deals with the relationship of domination parameters between $G_{uv}$ and $G$, and gets $\gamma(G_{uv})=\gamma(G)$ or $ \gamma(G_{uv})=\gamma(G)-1$, $\Gamma(G_{uv})=\Gamma(G)$ or $ \Gamma(G_{uv})=\Gamma(G)-1$, $\beta(G_{uv})=\beta(G)$ or $\beta(G_{uv})=\beta(G)-1$ . The sufficient and necessary conditions for $\gamma(G_{uv})=\gamma(G)-1$ and $\beta(G_{uv})=\beta(G)-1$ are also obtained. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2006.03.026 |
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