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arXiv · 1311.3049

The extremal problems on the inertia of weighted bicyclic graphs

Shibing Deng·Shuchao Li·Feifei Song
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Abstract

Let $G_w$ be a weighted graph. The number of the positive, negative and zero eigenvalues in the spectrum of $G_w$ are called positive inertia index, negative inertia index and nullity of $G_w$, and denoted by $i_{+}(G_w)$, $i_{-}(G_w)$, $i_{0}(G_w)$, respectively. In this paper, sharp lower bound on the positive (resp. negative) inertia index of weighted bicyclic graphs of order $n$ with pendant vertices is obtained. Moreover, all the weighted bicyclic graphs of order $n$ with at most two positive, two negative and at least $n-4$ zero eigenvalues are identified, respectively.

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Shibing Deng, Shuchao Li, Feifei Song. 2013-11-13. The extremal problems on the inertia of weighted bicyclic graphs. https://arxiv.org/abs/1311.3049

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