  Letters $x$ and $y$ alternate in a word $w$ if after deleting in $w$ all
letters but the copies of $x$ and $y$ we either obtain a word $xyxy\cdots$ (of
even or odd length) or a word $yxyx\cdots$ (of even or odd length). A graph
$G=(V,E)$ is word-representable if and only if there exists a word $w$ over the
alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if
$xy\in E$. It is known that a graph is word-representable if and only if it
admits a certain orientation called semi-transitive orientation.
  Word-representable graphs generalize several important classes of graphs such
as $3$-colorable graphs, circle graphs, and comparability graphs. There is a
long line of research in the literature dedicated to word-representable graphs.
However, almost nothing is known on word-representability of split graphs, that
is, graphs in which the vertices can be partitioned into a clique and an
independent set. In this paper, we shed a light to this direction. In
particular, we characterize in terms of forbidden subgraphs word-representable
split graphs in which vertices in the independent set are of degree at most 2,
or the size of the clique is 4. Moreover, we give necessary and sufficient
conditions for an orientation of a split graph to be semi-transitive.
