This paper studies the algorithms for coding and decoding Prufer codes of a labeled tree. The algorithms for coding and decoding Prufer codes of a labeled tree in the literatures require time usually. Although there exist linear time algorithms for Prufer-like codes [1,2,3], the algorithms utilize the integer sorting algorithms. The special range of the integers to be sorted is utilized to obta...

Invertibility of multiplication modules All rings are commutative with 1 and all modules are unital. Let R be a ring and M an R-module. M is called multiplication if for each submodule N of M, N=IM for some ideal I of R. Multiplication modules have recently received considerable attention during the last twenty years. In this talk we give the de nition of invertible submodules as a natural gene...

Many of the network topology design problems include CMST, which means to find a minimum cost tree that connects all the nodes of the network to the central node with some capacity constraint. The links of edges have associated costs that could be based on their distance, capacity, quality of line etc, and the nodes have their associated demand. Usually most of the network obtained from CMST ar...

Presented to the Society, December, 1955 under the title ^4 necessary condition for nonoscillation of a system of second order differential equations, and August, 1956; received by the editors August 2, 1956. 1 These results were obtained while the author held a National Science Foundation grant, NSF-G1825 and was at Yale University. Now at the University of Utah. 2 This paper contains a biblio...