Algebraic Graph Theory Seminar - Tereza Škublová (2.10.2026)

Friday 2.10.2026 at 13:15, Lecture room M IX (online too)

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Tereza Škublová:
On distance magic circulants of valency 2k for odd k

Abstract:
A circulant Circ(n,S) is a Cayley graph Cay(G,S), where G is the finite cyclic group Z_n. We assume that 0 ∉ S, S = −S and [S] = Z_n. A circulant Γ = Circ(n,S) is called distance magic if there exists a bijection ℓ from vertex set of Γ to the set {1,2,...,n} such that for each vertex x the sum of values of function ℓ through the vertices adjacent to vertex x is constant for all vertices x of Γ. Štefko MiklaviČ and Primož Šparl gave us a partial classification of the 6-regular distance magic circulants in their article On distance magic circulants of valency 6, Discrete Ap plied Mathematics, 2022. In this talk we give a brief overview of their results and discuss generalizations of their theorems to 2k-regular circulants for an odd k.

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