This paper introduces a family of simple bipartite graphs denoted by , named and constructed as polygon graphs. These polygon graphs are bicubic simple graphs possessing Hamiltonian cycles. Some important results are proved for these graphs. The girth of these graphs is counted as 6(). Polygon graph is isomorphic to a famous Pappus graph. Since polygon graphs are bipartite, therefore they can be used as Tanner graphs for low density parity check codes. This family of graphs may also be used in the design of efficient computer networks. Key words: Polygon graph, girth, Hamiltonian cycle, bicubic graph.