粘合运算对图的控制参数的影响

简单图G的粘合运算G_(uv)指的是重合G的两个顶点{u,v}并且去掉重边和环所得到简单图的运算．本文考虑了粘合运算对图的4个控制参数γ(G),Γ(G),β(G),i(G)的影响．刻画了图G_(uv)与图G的控制参数γ(G),Γ(G),γ(G),i(G)之间的关系．及给出γ(G_(uv))=γ(G)-1和β(G_(uv)=β(G)-1的充要条件．

Domination Parameters and Vertex-Contraction-Critical Graphs

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.