On the edge chromatic vertex stability number of graphs
Saeid Alikhani, Mohammad Reza Piri · AKCE International Journal of Graphs and Combinatorics · 2022
AbstractFor an arbitrary invariant [Formula: see text] of a graph G, the [Formula: see text]vertex stability number [Formula: see text] is the minimum number of vertices of G whose removal results in a graph [Formula: see text] with [Formula: see text] or with [Formula: see text] 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, [Formula: see text] where [Formula: see text] is edge chromatic number (chromatic index) of G. We prove some general results for this parameter and determine [Formula: see text] for specific classes of graphs.