We have investigated the properties of a group of Delta *g-ray-emitting globular clusters (GCs) that have recently been uncovered in our Galaxy. By correlating the observed Delta *g-ray luminosity L Delta *g with various cluster properties, we probe the origin of the high-energy photons from these GCs. We report that L Delta *g is positively correlated with the encounter rate Delta *G c and the metallicity Fe/H, which places an intimate link between the Delta *g-ray emission and the millisecond-pulsar population. We also find a tendency that L Delta *g increases with the energy densities of the soft photon at the cluster location. Furthermore, the two-dimensional regression analysis suggests that L Delta *g, soft-photon densities, and Delta *G c /Fe/H possibly span fundamental planes; this finding could potentially provide better predictions for the Delta *g-ray properties of GCs.