This paper describes an intuitive way of defining geometry design variables for solving structural topology optimization problems using a genetic algorithm (GA). The geometry representation scheme works by defining a skeleton that represents the underlying topology/connectivity of the continuum structure. As the effectiveness of any GA is highly dependent on the chromosome encoding of the design variables, the encoding used here is a directed graph which reflects this underlying topology so that the genetic crossover and mutation operators of the GA can recombine and preserve any desirable geometric characteristics through succeeding generations of the evolutionary process. The overall optimization procedure is tested by solving a simulated topology optimization problem in which a 'target' geometry is pre-defined with the aim of having the design solutions converge towards this target shape. The procedure is also applied to design a straight-line compliant mechanism : a large displacement flexural structure that generates a vertical straight line path at some point when given a horizontal straight line input displacement at another point. / Singapore-MIT Alliance (SMA)