ALEXANDER POLYNOMIAL FOR EVEN GRAPHS WITH REFLECTIVE SYMMETRY

Based on the connection with Alexander polynomial of special alternating links, Murasugi and Stoimenow introduced the Alexander polynomial of even graphs. In this paper, we study the Alexander polynomial of spatial even graphs with reflective symmetry. Roughly speaking, we prove that the Alexander polynomial of one half of a spatial even graph with reflective symmetry is a divisor of that of the whole spatial even graph. Then, we apply the result to a family of special alternating links, expressing the Alexander polynomial of such a link as the product of Alexander polynomials of two smaller special alternating links derived from the two isotopic "halves" of the original link.