Geodesic
The algebraic connectivity of two trees connected by an edge of infinite weight
The electronic journal of linear algebra, Tome 8 (2001), pp. 1-13.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 5C50, 15A48
Keywords: weighted tree, Laplacian matrix, algebraic connectivity, electrical circuit 
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     title = {The algebraic connectivity of two trees connected by an edge of infinite weight},
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Molitierno, Jason J.; Neumann, Michael. The algebraic connectivity of two trees connected by an edge of infinite weight. The electronic journal of linear algebra, Tome 8 (2001), pp. 1-13. http://geodesic.mathdoc.fr/item/ELA_2001__8__a11/