Group connectivity in $$J_3$$ J 3 line graphs

Abstract

Jaeger et al. (J Comb Theory Ser B 56:165---182, 1992) conjectured that every 5-edge-connected graph is $$Z_3$$Z3-connected. Moreover, Lai et al. (Discret Math 311:2295---2307, 2011) proved that every 5-edge-connected graph is $$Z_3$$Z3-connected if and only if every 5-edge-connected line graph is $$Z_3$$Z3-connected. A graph $$G$$G is a $$J_3$$J3 graph if every edge of $$G$$G lies in a 3-cycle of $$G$$G. We prove that every 5-edge-connected $$J_3$$J3 line graph is $$Z_3$$Z3-connected.