On the positive and negative inertia of weighted graphs

Abstract

The number of the positive, negative and zero eigenvalues in the spectrum of the (edge)-weighted graph $G$ are called positive inertia index, negative inertia index and nullity of the weighted graph $G$, and denoted by $i_{+}(G)$, $i_{-}(G)$, $i_0(G)$, respectively. In this paper, the positive and negative inertia index of weighted trees, weighted unicyclic graphs and weighted bicyclic graphs are discussed, the methods of calculating them are obtained.

12. arXiv admin note: text overlap with arXiv:1107.0400 by other authors

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