Degree-1 Vassiliev Invariant Of Virtual Knot And Biquandle Longitude Invariant Of Long Virtual Knot

In this paper,we first construct a Degree-1 Vassiliev invariant (?) based on the virtual link polynomial invariant RD constructed by Y.Miyazawa for DVMG graphs.Secondly,according to the two b operations S and S-1 defined by switch,the equivalence relationship that S and S-1 must satisfy is specified.we discuss the equivalence relation of any two elements on birack X and the equivalence relation of any three elements on biquandle X,and prove that biquandle coloring is a long virtual knot invariant.Finally,a basic quand/e Q(K)is given for a long virtual knot graph D.It is proved that Q(K)is a long virtual link invariant.The definition of quandle longitude of long knots is extended to long virtual knots and long virtual links.It is proved that the generalized quandle longitude is an invariant of long virtual knots and long virtual links.At the same time,an example of different long virtual links obtained by breaking the same virtual link at different points is given by using this invariant.