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Coalescing Fiedler and core vertices

Didar A. AliJohn Baptist GauciIrene ScirihaKhidir R. Sharaf — 2016

Czechoslovak Mathematical Journal

The nullity of a graph G is the multiplicity of zero as an eigenvalue in the spectrum of its adjacency matrix. From the interlacing theorem, derived from Cauchy’s inequalities for matrices, a vertex of a graph can be a core vertex if, on deleting the vertex, the nullity decreases, or a Fiedler vertex, otherwise. We adopt a graph theoretical approach to determine conditions required for the identification of a pair of prescribed types of root vertices of two graphs to form a cut-vertex of unique...

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