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On the spread of outerplanar graphs

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2022Embargo end date: 01 Jan 2021 English Publisher:Walter de Gruyter GmbHJournal:Special Matrices, volume 10, pages 299-307 (eissn: 2300-7451,

Authors: Gotshall Daniel; O’Brien Megan; Tait Michael;

doi: 10.1515/spma-2022-0164 , 10.48550/arxiv.2111.11820

arXiv: http://arxiv.org/abs/2111.11820

On the spread of outerplanar graphs

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Abstract

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 n , the n n -vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with Ω ( n ) \Omega \left(n) edges. We conjecture that the extremal graph is a vertex joined to a path on n − 1 n-1 vertices.

Related Organizations

Villanova University
United States

Keywords

outerplanar, adjacency eigenvalues, QA1-939, FOS: Mathematics, spread, Mathematics - Combinatorics, Combinatorics (math.CO), 05c50, Mathematics

3 Research products, page of 1

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Fields of Science

natural sciences

computer and information sciences

Fields of Science

natural sciences

computer and information sciences

Funded by

NSF| Algebraic Methods in Extremal Combinatorics