Dynamic Redundancy Bit Allocation and Packet Size to Increase Throughput in Noisy Real Time Video Wireless Transmission

When all vertices have the same weight, say w(x) = m for every x, then f is called distance magic labeling and G is a distance magic graph. It turns out that this type of magic labeling is very restrictive and consequently even many classes of the most “symmetric” graphs are not distance magic. As an example, we prove that for d ≡ 0, 1, 3 (mod 4) the hypercube Qd with 2d vertices is not distance magic. On the other hand, we disprove a conjecture by Acharya, Rao, Singh and Parameswaran, who believed that hypercubes are not distance magic except Q2 and present a distance magic labeling for Q6 and conjecture that it exists for every d ≡ 2 (mod 4). Such negative results then give rise a question whether it would not be more natural to perform the addition in Zn rather than in Z. Graphs that satisfy the above definition with the provision that the addition is performed in Zn will be called Zn-distance magic. To support this idea, we show some examples of graphs that are not distance magic yet are Zndistance magic. We show that when we perform addition Z16 rather than in Z, then for every m = 2, 6, 10, 14 there exists a labeling fm of Q4 such that the weight of every vertex is equal to m. We show examples of Zn-distance magic labelings of products of cycles and pose several open problems. This is in part a joint work with Christian Barrientos, Sylwia Cichacz, Elliot Krop and Christopher Raridan.