The Algebraic Connectivity of Graphs with Given Matching Number.

The algebraic connectivity of a graph is the second smallest eigenvalue of the associated Laplacian matrix. In this paper, we not only characterize the extremal graphs with the maximal algebraic connectivity among all graphs of order n with given matching number, but also determine the extremal tree with the maximal algebraic connectivity among all trees of order n with given matching number. [ABSTRACT FROM AUTHOR]