So, you're an application author, and want to install application icons so that they work in the KDE and Gnome menus. Minimally you should install a 48x48 icon in the hicolor theme. This means installing a PNG file in $prefix/share/icons/hicolor/48x48/apps. Optionally you can install icons in different sizes. For example, installing a svg icon in $prefix/share/icons/hicolor/scalable/apps means most desktops will have one icon that works for all sizes. You might even want to install icons with a look that matches other well known themes so your application will fit in with some specific desktop environment.

It is recommended that the icons installed in the hicolor theme look neutral, since it is a fallback theme that will be used in combination with some very different looking themes. But if you don't have any neutral icon, please install whatever icon you have in the hicolor theme so that all applications get at least some icon in all themes.