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arXiv · 2601.01164

Extremal $Q$-index problem in outerplanar graphs

Jin Cai·Leyou Xu·Bo Zhou
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Abstract

Outerplanar Turán problem has received considerable attention recently. We study the spectral version via $Q$-index. We determine the unique graph that maximizes the $Q$-index among all $n$-vertex connected outerplanar graphs which are respectively forbidden to contain: (i) a fixed cycle; and (ii) the disjoint union of paths of a given order.

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Jin Cai, Leyou Xu, Bo Zhou. 2026-01-03. Extremal $Q$-index problem in outerplanar graphs. https://arxiv.org/abs/2601.01164

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