We investigate the radial color gradients of galactic disks using a sample of ∼ 20, 000 face-on spiral galaxies selected from the fourth data release of the Sloan Digital Sky Survey (SDSS-DR4). We combine galaxies with similar concentration, size and luminosity to construct composite galaxies, and then measure their color profiles by stacking the azimuthally averaged radial color profiles of all the member galaxies. Except for the smallest galaxies (R 50 < 3 kpc), almost all galaxies show negative disk color gradients with mean g − r gradientḠ gr = −0.006 mag kpc −1 and r − z gradientḠ rz = −0.018 mag kpc −1 . The disk color gradients are independent of the morphological types of galaxies and strongly dependent on the disk surface brightness µ d , with lower surface brightness galactic disks having steeper color gradients. We quantify the intrinsic correlation between color gradients and surface brightness as G gr = −0.011µ d +0.233 and G rz = −0.015µ d + 0.324. These quantified correlations provide tight
A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 12p is given for each prime p. As a result, a connected pentavalent symmetric graph of order 12p exists if and only if p = 2, 3, 5 or 11, and up to isomorphism, there are only nine such graphs: one for each p = 2, 3 and 5, and six for p = 11.
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