This paper presents a significant advancement in micro-perforated panel absorber technologies. Two distinct types of sub-wavelength multi-chamber micro-perforated panel absorbers (MC-MPPA) for low-frequency broadband noise absorption under both normal and grazing acoustic incidence conditions are developed. Micro-perforated panel absorbers (MPPAs) exhibit versatility, eco-friendliness, and a straightforward, robust construction, making them ideal acoustic solutions. A graph-theory-based two-point impedance method (TpIM) and the Cremer impedance method are used for system modeling, enabling the design of the MC-MPPA to be optimized for maximum sound absorption in a chosen frequency range for both normal and grazing acoustic incidence. This graph theory approach represents a breakthrough, as an equivalent circuit model approach could not be applied to such complex models. Under normal incidence conditions, the experimental overall absorption coefficient is measured to be 0.8273 for a 22 mmthick MC-MPPA in the frequency range of [660 2000] Hz, and 0.8284 for a 52 mm thick MC-MPPA in the frequency range of [400 2000] Hz. Under grazing incidence conditions, an optimized MC-MPPA with a mere 30 mm sub-chamber depth achieves a transmission loss of 66 dB at 1180 Hz. Additionally, a 50 mm sub-chamber depth yields a transmission loss greater than 10 dB over an 880 Hz wide frequency range: [820 1700] Hz. The developed MC-MPPA technologies hold great promise for various duct noise attenuation applications including aeroengine acoustic liners.