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Many topology-dependent transmission scheduling algorithms have been proposed to minimize the time-division multiple-access frame length in multihop packet radio networks (MPRNs), in which changes of the topology inevitably require recomputation of the schedules. The need for constant adaptation of schedules-to-mobile topology entails significant problems, especially in highly dynamic mobile environments. Hence, topology-transparent scheduling algorithms have been proposed, which utilize Galois field theory and Latin squares theory. We discuss the topology-transparent broadcast scheduling design for MPRNs. For single-channel networks, we propose the modified Galois field design (MGD) and the Latin square design (LSD) for topology-transparent broadcast scheduling. The MGD obtains much smaller minimum frame length (MFL) than the existing scheme while the LSD can even achieve possible performance gain when compared with the MGD, under certain conditions. Moreover, the inner relationship between scheduling designs based on different theories is revealed and proved, which provides valuable insight. For topology-transparent broadcast scheduling in multichannel networks, in which little research has been done, the proposed multichannel Galois field design (MCGD) can reduce the MFL approximately M times, as compared with the MGD when M channels are available. Numerical results show that the proposed algorithms outperform existing algorithms in achieving a smaller MFL.