The Maximum Spectral Radius of Graphs Without Friendship Subgraphs

A graph on 2k + 1 vertices consisting of k triangles which intersect in exactly one common vertex is called a k−friendship graph and denoted by Fk. This paper determines the graphs of order n that have the maximum (adjacency) spectral radius among all graphs containing no Fk, for n sufficiently large. Mathematics Subject Classifications: 05C50; 05C38 ∗S. M. Cioabă is partially supported by NSF grants DMS-1600768 and CIF-1815922 and a JSPS Fellowship. †L. Feng is partially supported by NSFC (Nos. 11871479, 11671402), Hunan Provincial Natural Science Foundation (2016JJ2138, 2018JJ2479) and Mathematics and Interdisciplinary Sciences Project of CSU. ‡M. Tait is partially supported by NSF grant DMS-2011553. §X.-D. Zhang is partially supported by NSFC (Nos. 11971311, 11531001); the Montenegrin-Chinese Science and Technology Cooperation Project (No.3-12) (Corresponding author). the electronic journal of combinatorics 27(4) (2020), #P4.22 https://doi.org/10.37236/9179

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