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
Usage 71
Downloads 58
Abstract Views 13
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:
10.13001/1081-3810.1056
Author(s):
Molitierno, Jason J.; Neumann, Michael
Publisher(s):
University of Wyoming Libraries
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.