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Each knot invariant can be extended to singular knots according to the skeinrule. A Vassiliev invariant of order at most $n$ is defined as a knot invariantthat vanishes identically on knots with more than $n$ double points. A chorddiagram encodes the order of double points along a singular knot. A Vassilievinvariant of order $n$ gives rise to a function on chord diagrams with $n$chords. Such a function should satisfy some conditions in order to come from aVassiliev invariant. A weight system is a function on chord diagrams thatsatisfies so-called 4-term relations. Given a Lie algebra $\mathfrak{g}$equipped with a non-degenerate invariant bilinear form, one can construct aweight system with values in the center of the universal enveloping algebra$U(\mathfrak{g})$. In this paper, we calculate $\mathfrak{sl}_3$ weight systemfor chord diagram whose intersection graph is complete bipartite graph$K_{2,n}$.

On values of $\mathfrak{sl}_3$ weight system on chord diagrams whose intersection graph is complete bipartite