Geodesic
Nullity of Graphs: An Updated Survey
Zbornik radova, Tome 14 (2011) no. 22, p. 137

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The nullity $\eta=\eta(G)$ of a graph $G$ is the multiplicity of the number zero in the spectrum of $G$\,. The chemical importance of this graph-spectrum based invariant lies in the fact, that within the Hückel molecular orbital model, if $\eta(G)>0$ for the molecular graph $G$\,, then the corresponding chemical compound is highly reactive and unstable, or nonexistent. This chapter in an updated version of the an earlier survey [B. Borovićanin, I. Gutman, \emph{Nullity of graphs}, in: D. Cvetković, I. Gutman, Eds. \emph{Applications of Graph Spectra}, Math. Inst., Belgrade, 2009, pp. 107-122] and outlines both the chemically relevant aspects of $\eta$ (most of which were obtained in the 1970s and 1980s) and the general mathematical results on $\eta$ obtained recently.
Classification : 05C50 05C90 92E10
Keywords: zero eigenvalue (of graph), spectrum (of graph), chemistry 
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     author = {Ivan Gutman and Bojana Borovi\'canin},
     title = {Nullity of {Graphs:} {An} {Updated} {Survey}},
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Ivan Gutman; Bojana Borovićanin. Nullity of Graphs: An Updated Survey. Zbornik radova, Tome 14 (2011) no. 22, p. 137 . http://geodesic.mathdoc.fr/item/ZR_2011_14_22_a5/