The algebraic connectivity of two trees connected by an edge of infinite weight
Electron. J. Linear Algebra 8, 1-13, electronic only (2001)
Summary
Summary: Let T 1 and T 2 be two weighted trees with algebraic connectivities _(T 1 ) and _(T 2 ), respectively. A vertex on one of the trees is connected to a vertex on the other by an edge of weight w to obtain a new tree ^ T w . By interlacing properties of eigenvalues of symmetric matrices it is known that _( ^ T w ) ^ $minf_(T 1 )$; _(T 2 )g =: m . It is determined precisely when _( ^ T w ) ! m as w ! 1. Finally, a possible interpretation is given of this result to the theory of electrical circuits and Kirchoff's laws.
