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arXiv · 2111.11820

On the spread of outerplanar graphs

Daniel Gotshall·Megan O'Brien·Michael Tait
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Abstract

The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large $n$, the $n$-vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with $Ω(n)$ edges. We conjecture that the extremal graph is a vertex joined to a path on $n-1$ vertices.

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Daniel Gotshall, Megan O'Brien, Michael Tait. 2021-11-23. On the spread of outerplanar graphs. https://arxiv.org/abs/2111.11820

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