Clique-Number of Timbral Graphs
Márcia R. Cerioli, Luan Simões Cardoso, Petrúcio Viana · 2024
We study the clique-number of the timbral graphs Tn,k,ℓ. The vertex set of Tn,k,ℓ is the set of all words of length k built on an alphabet of n symbols and two vertices are adjacent when they agree in exactly ℓ coordinates. We provide lower and upper bounds for the general case and determine ω(Tn,k,1) when k−1 ≤ n is a prime power, showing the correspondence between a clique with n2 vertices in Tn,n+1,1 and an affine plane of order n.