Spectral extrema of graphs forbidding a fan

2025/08/08 by Wenqian Zhang, Zhang, Wenqian · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2508.05911

openalex publication_date 2025/08/08 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

For a graph G, its spectral radius is the largest eigenvalue of its adjacency matrix. A fan H_ℓ is a graph obtained by connecting a single vertex to all vertices of a path of order ℓ≥4. Let \rm SPEX(n,H_ℓ) be the set of all extremal graphs G of order n with the maximum spectral radius, where G contains no H_ℓ as a subgraph. In this paper, we completely characterized the graphs in \rm SPEX(n,H_ℓ) for any ℓ≥4 and sufficiently large n. An interesting phenomenon was revealed: \rm SPEX(n,H_2k+2)⊆ \rm SPEX(n,H_2k+3) for any k≥1 and sufficiently large n.

Citations

• Spectral Turán problem of non-bipartite graphs: Forbidden books
• Spectral radius of graphs of given size with forbidden a fan graph F₆
• Spectral extrema of graphs with fixed size: forbidden a fan graph, friendship graph or theta graph
• More results on the spectral radius of graphs with no odd wheels
• Spectral extremal graphs for fan graphs
• A general theorem in spectral extremal graph theory
• Spectral extremal results on edge blow-up of graphs
• Spectral extremal problem on the square of ℓ-cycle
• Spectral extremal graphs for disjoint cliques
• The spectral even cycle problem
• On a conjecture of spectral extremal problems
• Spectral radius, edge-disjoint cycles and cycles of the same length
• Spectral extremal graphs for intersecting cliques
• The spectral radius of graphs with no odd wheels
• A strengthening of the spectral chromatic critical edge theorem: books and theta graphs
• The maximum spectral radius of wheel-free graphs
• The Colin de Verdi `ere parameter, excluded minors, and the spectral\n radius
• The spectral radius of graphs without paths and cycles of specified length
• Spectral saturation: inverting the spectral Turan theorem
• Bounds on graph eigenvalues II

Cited by

• Spectral Turán problems for suspensions of balanced trees

Related

• A general theorem in spectral extremal graph theory
• Ordinary and spectral extremal problems on vertex disjoint copies of even fans
• Spectral extremal graphs for intersecting cliques
• A sharp spectral extremal result for general non-bipartite graphs
• Spectral skeletons and applications