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We show that graph map with zero topological entropy is Li-Yorke chaotic ifand only if it has an NS-pair (a pair of non-separable points containing in asame solenoidal $\omega$-limit set), and a non-diagonal pair is an NS-pair ifand only if it is an IN-pair if and only if it is an IT-pair. This completescharacterization of zero topological sequence entropy for graph maps.

Graph maps with zero topological entropy and sequence entropy pairs