This paper first surveys election algorithms on synchronous ring networks and then presents two algorithms for distributed election on synchronous networks in which processors have distinct identifiers taken from the countable set of natural numbers. Using an algorithm, which generalizes previous results for synchronous ring election and which exploits identifiers and clocks, a new O(e) worst case message complexity upper bound is demonstrated for networks of unknown topology. Unfortunately, the algorithm may suffer an exorbitant time complexity. In consequence, a more time-efficient second algorithm that incurs O(e log*n) message complexity is presented, where log*k is the number of times the log function must be applied to k to obtain a result less than or equal to 1. Synchronous distributed election on networks where processors do not have identifiers, i.e. the symmetry breaking problem, is also considered. A random algorithm for the general network which expects O(e) bit and time complexity assuming global knowledge of the number of processors and network links, is given, again generalizing past results for rings.