Some results on energy of unicyclic graphs with n vertices

摘要

A unicyclic graph is a connected graph whose number of edges is equal to the number of vertices. Hou (J Math Chem 29:163–168, 2001) first considered the minimal energy for general unicyclic graphs. In this paper, we determine the unicyclic graphs with the minimal energy in and the unicyclic graphs with the first forth smallest energy in vertices. Keywords Unicyclic graphs - Energy - Characteristic polynomial