The algebraic connectivity of two trees connected by an edge of infinite weight
 Citation data:

Electronic Journal of Linear Algebra, Vol: 8, Issue: 1
 Publication Year:
 2001

 Bepress 56

 Bepress 7
 Bepress 3
 Bepress 1
 Repository URL:
 https://digitalcommons.sacredheart.edu/math_fac/43; http://repository.uwyo.edu/ela/vol8/iss1/1; https://works.bepress.com/jason_molitierno/14
 DOI:
 10.13001/10813810.1056
 Author(s):
 Publisher(s):
 Tags:
 Mathematics
article description
Let T 1 and T 2 be two weighted trees with algebraic connectivities μ(T 1 ) and μ(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 μ(T ^ w )≤min{μ(T 1 ),μ(T 2 )}=:m. It is determined precisely when μ(T ^ w ) tends to m as w tends to infinity. Finally, a possible interpretation is given of this result to the theory of electrical circuits and Kirchoff’s laws.