Competition numbers of Halin graphs

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For any graph G, G together with sufficiently many isolated vertices is the competition graph of some acyclic digraph.The competition number k(G) of a graph G is defined to be the smallest number of such isolated vertices.In general, it is hard to compute the competition number k(G) for a graph G and characterizing a graph by its competition number has been one of important research problems in the study of competition graphs.A Halin graph is a planar graph consisting of a tree with no vertex of degree two and a cycle connecting the leaves of the tree.
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