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Creators/Authors contains: "Li, Zelong"

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  1. Free, publicly-accessible full text available October 3, 2026
  2. Free, publicly-accessible full text available November 12, 2025
  3. 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 $$\lceil(2n-1)/3\rceil$$ vertices and $$\lfloor(n-2)/3\rfloor$$ 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 $$\lceil(2n-2)/3\rceil$$ vertices and $$\lfloor(n-4)/3\rfloor$$ isolated vertices. 
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  4. null (Ed.)