Geodesic
Algebraic connectivity of trees with a pendant edge of infinite weight
The electronic journal of linear algebra, Tome 13 (2005), pp. 175-186.

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

Summary: Let G be a weighted graph. Let v be a vertex of G and let Gv! denote the graph obtained by adding a vertex u and an edge ${v, u}$ with weight ! to G. Then the algebraic connectivity $u(Gv!)$ of Gv! is a nondecreasing function of ! and is bounded by the algebraic connectivity $u(G)$ of G. The question of when lim!!$1 u(Gv!)$ is equal to $u(G)$ is considered and answered in the case that G is a tree.
Keywords: weighted graphs, trees, Laplacian matrix, algebraic connectivity, pendant edge 
@article{ELA_2005__13__a11,
     author = {Berman, A. and F\"orster, K.-H.},
     title = {Algebraic connectivity of trees with a pendant edge of infinite weight},
     journal = {The electronic journal of linear algebra},
     pages = {175--186},
     publisher = {mathdoc},
     volume = {13},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2005__13__a11/}
}
TY  - JOUR
AU  - Berman, A.
AU  - Förster, K.-H.
TI  - Algebraic connectivity of trees with a pendant edge of infinite weight
JO  - The electronic journal of linear algebra
PY  - 2005
SP  - 175
EP  - 186
VL  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ELA_2005__13__a11/
LA  - en
ID  - ELA_2005__13__a11
ER  - 
%0 Journal Article
%A Berman, A.
%A Förster, K.-H.
%T Algebraic connectivity of trees with a pendant edge of infinite weight
%J The electronic journal of linear algebra
%D 2005
%P 175-186
%V 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ELA_2005__13__a11/
%G en
%F ELA_2005__13__a11
Berman, A.; Förster, K.-H. Algebraic connectivity of trees with a pendant edge of infinite weight. The electronic journal of linear algebra, Tome 13 (2005), pp. 175-186. http://geodesic.mathdoc.fr/item/ELA_2005__13__a11/