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On the Yoshinaga polynomial of spatial graphs

An explicit relation between two well-known polynomial invariants of spatial graphs is established. If g is a diagram of a spatial graph with p vertices and q edges, then Y (g; t) = (−t− t−1)p− q R (g ′; t), where Y (g) is the Yoshinaga polynomial of g and R(g ′) is the Yamada polynomial of its mirror image g ′.