The maximum spectral radius of graphs without friendship subgraphs

DOI10.37236/9179zbMath1453.05059OpenAlexW3097178077MaRDI QIDQ2209893

Michael Tait, Sebastian M. Cioabă, Xiao Dong Zhang, Li-Hua Feng

Publication date: 5 November 2020

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.37236/9179

File on IPFS

zbMATH Keywords

spectral radiusadjacency matrixfriendship graph

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Paths and cycles (05C38) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (48)

Spectral extremal graphs for intersecting cliques ⋮ Signless Laplacian spectral radius of graphs without short cycles or long cycles ⋮ Spectral radius, edge-disjoint cycles and cycles of the same length ⋮ The spectral radius of graphs with no intersecting odd cycles ⋮ Generalizing theorems of Nosal and Nikiforov: triangles and quadrilaterals ⋮ A spectral condition for the existence of the square of a path ⋮ On the spectral radius of graphs without a star forest ⋮ The maximum spectral radius of wheel-free graphs ⋮ A unique characterization of spectral extrema for friendship graphs ⋮ Spectral extrema of \(K_{s,t}\)-minor free graphs -- on a conjecture of M. Tait ⋮ A strengthening of the spectral chromatic critical edge theorem: Books and theta graphs ⋮ Spectral extremal graphs for the bowtie ⋮ A Spectral Erdős-Sós Theorem ⋮ A complete solution to the Cvetković–Rowlinson conjecture ⋮ Refinement on Spectral Turán’s Theorem ⋮ On a conjecture of spectral extremal problems ⋮ The maximum spectral radius of graphs without spanning linear forests ⋮ Maxima of the \(Q\)-index of non-bipartite graphs: forbidden short odd cycles ⋮ Spectral radius of graphs of given size with forbidden subgraphs ⋮ The unique spectral extremal graph for intersecting cliques or intersecting odd cycles ⋮ Spectral extremal graphs for disjoint cliques ⋮ Spectral radius conditions for the existence of all subtrees of diameter at most four ⋮ Maximum degree and spectral radius of graphs in terms of size ⋮ Maxima of the \(Q\)-index of non-bipartite \(C_3\)-free graphs ⋮ Spectral extrema of \(\{ K_{k + 1}, \mathcal{L}_s \}\)-free graphs ⋮ Spectral Turán problems for intersecting even cycles ⋮ A spectral extremal problem on non-bipartite triangle-free graphs ⋮ Spectral extremal problem on disjoint color-critical graphs ⋮ Counting substructures and eigenvalues. I: Triangles ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The spectral radius of graphs with no intersecting triangles ⋮ Spectral extremal graphs for edge blow-up of star forests ⋮ The signless Laplacian spectral radius of graphs without intersecting odd cycles ⋮ The spectral even cycle problem ⋮ The spectral radius of graphs with no odd wheels ⋮ Spectral extremal graphs without intersecting triangles as a minor ⋮ The signless Laplacian spectral radius of graphs with no intersecting triangles ⋮ The signless Laplacian spectral radius of \(2K_3\)-free graphs ⋮ A spectral Erdős-Rademacher theorem ⋮ Spectral extrema of graphs with fixed size: forbidden triangles and pentagons ⋮ On the spectral radius of graphs without a gem ⋮ On the spectral Turán problem of theta graphs ⋮ Turán-type problems on \([a, b\)-factors of graphs, and beyond] ⋮ Spectral extremal problem on \(t\) copies of \(\ell\)-cycles ⋮ The \(\alpha \)-index of graphs without intersecting triangles/quadrangles as a minor ⋮ The spectral radius and \({\mathcal{P}}_{\ge \ell}\)-factors of graphs involving minimum degree ⋮ Maxima of the \(Q\)-index: forbidden a Fan

Cites Work

• Unnamed Item
• Unnamed Item
• A proof of the stability of extremal graphs, Simonovits' stability from Szemerédi's regularity
• A new proof of the graph removal lemma
• A contribution to the Zarankiewicz problem
• The spectral radius of graphs without paths and cycles of specified length
• Graphs with given diameter maximizing the spectral radius
• The asymptotic number of graphs not containing a fixed subgraph and a problem for hypergraphs having no exponent
• Degrees and matchings
• The spectral radius of graphs on surfaces
• Spectral radius and \(k\)-connectedness of a graph
• Eigenvalues of subgraphs of the cube
• A bound on the spectral radius of graphs with \(e\) edges
• On the spectral radius of graphs with cut vertices
• Extremal graphs for intersecting triangles
• What we know and what we do not know about Turán numbers
• Bounds on graph eigenvalues. II
• On the spectral radius of graphs with a given domination number
• On bags and bugs
• Intersection theorems for systems of sets
• Graph removal lemmas
• Some new results in extremal graph theory
• Some Inequalities for the Largest Eigenvalue of a Graph
• Matrix Analysis
• On the Spectral Radius of Complementary Acyclic Matrices of Zeros and Ones
• The Algorithmic Aspects of the Regularity Lemma
• Spectral conditions for graphs to be β-deficient involving minimum degree
• The History of Degenerate (Bipartite) Extremal Graph Problems
• Spectral radius and Hamiltonicity of graphs

This page was built for publication: The maximum spectral radius of graphs without friendship subgraphs