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Chen, Y., Li, S., Zhang, L. and Zhang, M. (2025) Spectral Extrema of F2-Free Graphs with Given Size Revisited. Discrete Applied Mathematics, 375, 294-307.https://doi.org/10.1016/j.dam.2025.06.007

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• TITLE: Spectral Extremal Graphs for the F3 Graph

  AUTHORS: Yizhi Yin

  KEYWORDS: F3-Free, Spectral Extremal Graph, Balanced Complete Bipartite Graph

  JOURNAL NAME: Applied Mathematics, Vol.17 No.5, May 29, 2026

  ABSTRACT: Let Fk be the (friendship) graph obtained from k triangles by sharing a common vertex. In 2024, Li, Lu, Peng [Discrete Mathematics 346(2023)] show that the unique n-vertex F2 -free spectral extremal graph is the balanced bipartite graph adding an edge in smaller part if n ≥7. Following their result, we show that the unique n-vertex F3-free spectral extremal graph is the balanced complete bipartite graph adding two disjoint K3 in the vertex part with smaller size if n > 360.