Geodesic
Nullity of Graphs: An Updated Survey
Zbornik radova, Tome 14 (2011) no. 22, p. 137 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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}},
     journal = {Zbornik radova},
     pages = {137 },
     year = {2011},
     volume = {14},
     number = {22},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZR_2011_14_22_a5/}
}
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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/