The diffuse ultraviolet background radiation has been mapped over most of the sky with 2arcmin resolution using data from the textit{GALEX} survey. We utilize this map to study the correlation between the UV background and clusters of galaxies discovered via the Sunyaev-Zeldovich effect in the textit{Planck} survey. We use only high Galactic latitude ($|b| > 60^{circ} $) galaxy clusters to avoid contamination by Galactic foregrounds, and we only analyze clusters with a measured redshift. This leaves us with a sample of 142 clusters over the redshift range $0.02 leq z leq 0.72$, which we further subdivide into four redshift bins. In analysing our stacked samples binned by redshift, we find evidence for a central excess of UV background light compared to local backgrounds for clusters with $z<0.3$. We then stacked these $z<0.3$ clusters to find a statistically significant excess of $12 pm 2.3$ photon cm$^{-2}$ s${-1}$ sr$^{-1}$ AA $^{-1}$ over the median of $sim 380$ photon cm$^{-2}$ s${-1}$ sr$^{-1}$ AA $^{-1}$ measured around random blank fields. We measure the stacked radial profile of these clusters, and find that the excess UV radiation decays to the level of the background at a radius of $sim 1$ Mpc, roughly consistent with the maximum radial extent of the clusters. Analysis of possible physical processes contributing to the excess UV brightness indicates that non-thermal emission from relativistic electrons in the intracluster medium and faint, unresolved UV emission from cluster member galaxies and intracluster light are likely the dominant contributors.
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