On the spread of outerplanar graphs

Special Matrices

Tait Michael¹  Gotshall Daniel¹  O’Brien Megan¹ 

[1] Department of Mathematics and Statistics, Villanova University, Pennsylvania, United States;

关键词: spread;    adjacency eigenvalues;    outerplanar;    05c50;   

DOI  :  10.1515/spma-2022-0164

来源: DOAJ

【 摘 要 】

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 nn, the nn-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−1n-1 vertices.

【 授权许可】

Unknown