For an arbitrary invariant $\rho (G)$ of a graph $G$, the $\rho-$vertex stability number $vs_{ \rho}(G)$ is the minimum number of vertices of $G$ whose removal results in a graph $H\subseteq G$ with $\rho (H)\neq \rho (G)$ or with $E(H)=\varnothing$. In this paper, first we give some general lower and upper bounds for the $\rho$-vertex stability number, and then study the edge chromatic stability number of graphs, $vs_{ \chi^{ \prime}}(G)$, where $\chi^{ \prime}=\chi^{ \prime}(G)$ is edge chromatic number (chromatic index) of $G$. We prove some general results for this parameter and determine $vs_{ \chi^{ \prime}}(G)$ for specific classes of graphs.
Categories: math.CO