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.