Spectral Extremal Graphs for the F 3 Graph

Abstract

Let F k 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 F 2 -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 F 3 -free spectral extremal graph is the balanced complete bipartite graph adding two disjoint K 3 in the vertex part with smaller size if n > 360.