Competition Numbers of a Kind of Pseudo-Halin Graphs

Abstract

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 2-connected planar graph G with minimum degree at least 3 is a pseudo-Halin graph if deleting the edges on the boundary of a single face 0 f yields a tree. It is a Halin graph if the vertices of 0 f all have degree 3 in G . In this paper, we compute the competition numbers of a kind of pseudo-Halin graphs.