Abstract: A subset S⊆V(G) is a K_1,2-isolating set, if R(S)=V\N[S] have isolated vertices and isolated edges only. The isolation number ι₁(G) of G is the minimum cardinality of a isolation set of G. Based on the relationship between the number of bad vertices k and the number of vertices of degree 2, using mathematical induction on n+k, $\iota_{1}(G) \leqslant \frac{n+k}{6}$ is proved for the maximal outerplanar graph G, and the upper bound of K_1,2-isolating number is further improved,where k is the number of pairs of consecutive vertices of degree 2 with distance at least 3 on the Hamiltonian cycle.

Key words: maximal outerplanar graph, K_1,2-isolating set, bad vertices