The Number of Labeled Outerplanar k-Cyclic Graphs
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A k-cyclic graph is a graph with cyclomatic number k. An explicit formula for the number of labeled connected outerplanar k-cyclic graphs with a given number of vertices is obtained. In addition, such graphs with fixed cyclomatic number k and a large number of vertices are asymptotically enumerated. As a consequence, it is found that, for fixed k, almost all labeled connected outerplanar k-cyclic graphs with a large number of vertices are cacti.
Keywordsenumeration labeled graph connected graph k-cyclic graph outerplanar graph cactus asymptotics
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