On the edge chromatic vertex stability number of graphs

Abstract

For an arbitrary invariant $\rho (G)$ of a graph $G$, the $\rho -$vertex stability number $v{s}_{\rho }(G)$ is the minimum number of vertices of $G$ whose removal results in a graph $H\subseteq G$ with $\rho (H)\ne \rho (G)$ 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, $v{s}_{{\chi }^{\prime }}(G)$, where ${\chi }^{\prime }={\chi }^{\prime }(G)$ is edge chromatic number (chromatic index) of $G$. We prove some general results for this parameter and determine $v{s}_{{\chi }^{\prime }}(G)$ for specific classes of graphs.

11 pages, 1 figure