Document Type

Article

Publication Date

1-1-2024

Abstract

The spread of a graph G is the difference between the largest and smallest eigenvalue of the adjacency matrix of G. Gotshall, O’Brien and Tait conjectured that for sufficiently large n, the n-vertex outerplanar graph with maximum spread is the graph obtained by joining a vertex to a path on n − 1 vertices. In this paper, we disprove this conjecture by showing that the extremal graph is the graph obtained by joining a vertex to a path on ⌈(2n − 1)/3⌉ vertices and ⌊(n − 2)/3⌋ isolated vertices. For planar graphs, we show that the extremal n-vertex planar graph attaining the maximum spread is the graph obtained by joining two nonadjacent vertices to a path on ⌈(2n − 2)/3⌉ vertices and ⌊(n − 4)/3⌋ isolated vertices.

Publication Source (Journal or Book title)

Electronic Journal of Combinatorics

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