The inertia of unicyclic graphs and the implications for closed-shells |
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Authors: | Sean Daugherty |
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Institution: | Department of Computer Science, University of Victoria, Victoria, BC, Canada V8W 3P6 |
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Abstract: | The inertia of a graph is an integer triple specifying the number of negative, zero, and positive eigenvalues of the adjacency matrix of the graph. A unicyclic graph is a simple connected graph with an equal number of vertices and edges. This paper characterizes the inertia of a unicyclic graph in terms of maximum matchings and gives a linear-time algorithm for computing it. Chemists are interested in whether the molecular graph of an unsaturated hydrocarbon is (properly) closed-shell, having exactly half of its eigenvalues greater than zero, because this designates a stable electron configuration. The inertia determines whether a graph is closed-shell, and hence the reported result gives a linear-time algorithm for determining this for unicyclic graphs. |
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Keywords: | 58C40 92E10 05C85 05C70 |
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