SOME EXTREMAL RESULTS ON THE CHROMATIC STABILITY INDEX

Abstract The $\chi $ -stability index $\mathrm {es}_{\chi }(G)$ of a graph G is the minimum number its edges whose removal results in with chromatic smaller than that . We consider three open problems from Akbari et al. [‘Nordhaus–Gaddum and other bounds for edge-stability number’, European J. Combin. 84 (2020), Article no. 103042]. show by examples known characterisation k -regular ( $k\le 5$ ) graphs }(G) = 1$ does not extend to $k\ge 6$ , we characterise (G)=3$ which { es}_{\chi }(G)+\mathrm }(\overline {G}) 2$ derive necessary conditions on attain upper bound terms order are sufficient when $n\equiv 2 \pmod 3$