We study edge complexity, the minimum Fourier $\ell^1/\ell^2$ ratio of a graph's adjacency matrix over cyclic vertex labelings. For $K_{m,n}$, with $1\leq m\leq n$, we reduce the problem to minimizing the Fourier $\ell^1$-norm of indicators of $m$-element subsets of $\mathbb Z_{m+n}$. We prove the sharp bound $\operato...
S. Ferguson, V. Gupta, A. Iosevich et al.· 0 citations
We study the additive energy and the Fourier approximation of graph adjacency matrices labeled by a cyclic group. For a graph with $N$ vertices, $s$ edges and adjacency matrix $M$, the additive energy of its directed edge set is at most $\min\{(2s)^3,N^2\operatorname{tr}(M^4)\}$, and equality in the spectral bound hold...
V. Gupta, S. Ferguson, A. Iosevich et al.· 0 citations
The edge complexity of a weighted graph is the smallest ratio of the Fourier $\ell^1$ and $\ell^2$ norms of its adjacency matrix over all vertex labelings. We study the difficulty of finding this minimum by relating it to a graph symmetry. Adding a universal vertex with sufficiently large incident weight produces an ex...
Gupta and Iosevich introduced the edge complexity of a graph as the minimum Fourier ratio of its adjacency matrix over all vertex labelings and bounded it below by graph energy divided by the square root of twice the number of edges. We characterize equality for a fixed labeling: the Fourier transform of the adjacency...
Vishal Gupta, A. Iosevich, J. Iosevich et al.· 0 citations
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