Multiplicative and mining property for stability numbers of graphs

Abstract

$f$-vertex stability number $v{s}_f(G)=\min \{|X|:X\subseteq V(G)\text{and}f(G-X)\ne f(G)\}$, and $f$-edge stability number is defined similarly by setting $X\subseteq E(G)$. In this paper, for multiplicative and mining invariant $f$, we give some general bounds for $f$-vertex/edge stability numbers of graphs and some results about the relations between the $f$-vertex/edge stability numbers of graphs and their components.