The Kirchhoff indices and the matching numbers of unicyclic graphs

摘要

The Kirchhoff index of a connected graph is the sum of resistance distancesbetween all unordered pairs of vertices in the graph. It found considerableapplications in a variety of fields. In this paper, we determine the minimumKirchhoff index among the unicyclic graphs with fixed number of vertices andmatching number, and characterize the extremal graphs.