Abstract

A subset S of vertices in a graph G is called an isolating set if V(G)∖NG[S] is an independent set of G. The isolation number ι(G) is the minimum cardinality of an isolating set of G. Let G be a maximal outerplanar graph of order n with n2 vertices of degree 2. It was previously proved that ι(G)≤n4. In this paper, we improve this bound to be ι(G)≤n+n25whenn2≤n4,n−n23otherwise,and these bounds are best possible.

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