Geodesic
Nullity of Graphs
Zbornik radova, Tome 13 (2009) no. 21, p. 107

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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 H$\ddot{u}$ckel 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 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: nullity (of graph), zero eigenvalue (of graph), spectrum (of graph), chemistry 
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     author = {Bijana Borovi\'canin and Ivan Gutman},
     title = {Nullity of {Graphs}},
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     number = {21},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZR_2009_13_21_a4/}
}
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Bijana Borovićanin; Ivan Gutman. Nullity of Graphs. Zbornik radova, Tome 13 (2009) no. 21, p. 107 . http://geodesic.mathdoc.fr/item/ZR_2009_13_21_a4/