On the edge chromatic vertex stability number of graphs

Abstract

For an arbitrary invariant of a graph G, the vertex stability number is the minimum number of vertices of G whose removal results in a graph with or with In this paper, first we give some general lower and upper bounds for the ρ-vertex stability number, and then study the edge chromatic vertex stability number of graphs, where is edge chromatic number (chromatic index) of G. We prove some general results for this parameter and determine for specific classes of graphs.