In this article, we present an efficient algorithm for encoding the connectivity information of general polygon meshes. The algorithm is a single-resolution lossless compression method for meshes, mainly for non-triangular meshes. In comparison with the excellent algorithms previously proposed for non-triangular meshes, the new method highly improves the compression ratio by using a novel entropy coding method. By the method, Huffman coder is first applied, then a context-based arithmetic coder is employed to encode the Huffman codes.The new method also puts forward a novel mesh traversing method by which the traversal to each polygon face could be in multiple times, though encoding each face is still only once. In this new method, "jump" operations are added to replacing "split" operations commonly used in various existing connectivity compression algorithms. Much of the decoding time and space could be saved by using the new traversing method through taking advantage of a decoding scheme that the operator code could be immediately discarded as soon as it is decoded. Therefore, the decoding method could be well applied to the applications with online transmission and decoding. In another word, our algorithm has an advantage of parallel encoding and decoding. The algorithm is also capable of handling the meshes with holes.