Geodesic
On the characterization of graphs with pendent vertices and given nullity
The electronic journal of linear algebra, Tome 18 (2009), pp. 719-734.

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

Summary: Let G be a graph with n vertices. The nullity of G, denoted by $\eta (G)$, is the multiplicity of the eigenvalue zero in its spectrum. In this paper, we characterize the graphs (resp. bipartite graphs) with pendent vertices and nullity $\eta $, where $0 \eta \leq n$. Moreover, the minimum (resp. maximum) number of edges for all (connected) graphs with pendent vertices and nullity $\eta $are determined, and the extremal graphs are characterized.
Classification : 05C50
Keywords: eigenvalue, nullity, pendent vertex 
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     title = {On the characterization of graphs with pendent vertices and given nullity},
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Liu, Bolian; Huang, Yufei; Chen, Siyuan. On the characterization of graphs with pendent vertices and given nullity. The electronic journal of linear algebra, Tome 18 (2009), pp. 719-734. http://geodesic.mathdoc.fr/item/ELA_2009__18__a6/