Semiharmonic bicyclic graphs

Let the trunk of a graph G be the graph obtained by removing all leaves of G. We prove that, for every integer c 2, there are at most finitely many trunks of semiharmonic graphs with cyclomatic number c -- in contrast to the fact established by the last two of the present authors in their paper Semiharmonic Bicyclic Graphs (this journal) that there are infinitely many connected semiharmonic graphs with given cyclomatic number. Further, we prove that there are at most finitely many semiharmonic but not almost semiregular graphs with cyclomatic number c. MSC Classification: 05C75

• Type: Journal
• Year: 2005
• Where: APPML
• Authors: Stefan Grünewald, Dragan Stevanovic
• Keywords: APPML 2005, Cyclomatic Number, Semiharmonic Bicyclic Graphs, Semiharmonic Graphs