Abstract
The cycles in an interconnection network are one of the communication types that are considered as a factor to measure the efficiency and reliability of the networks’ topology. The network is said to be panconnected if there are cycles of length l between two nodes u and v, for all l = d(u, v), d(u, v) + 1, d(u, v) + 2, …, n − 1 where d(u, v) is the shortest distance between u and v in a given network, and n is the total number of nodes in the network. In this paper, we propose an algorithm that proves the existence of panconnectivity of Eisenstein-Jacobi networks by constructing all cycles between any two nodes in the network of length l such that 3 ≤ l < n. The correctness of the proposed algorithm is given with the time complexity O(n4). The proposed algorithm adopts and modifies the idea of Dynamic Source Routing (DSR) to find all possible shortest paths. The results of some test cases using the proposed algorithm are provided.
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