Word-representability of split graphs generated by morphisms

A graph G=(V,E) is word-representable if and only there exists a word w over the alphabet V such that letters x y, x≠y, alternate in xy∈E. split which vertices can be partitioned into clique an independent set. There long line of research on graphs literature, recently, word-representability has attracted interest. In this paper, we first give characterization terms permutations columns adjacency matrices. Then, focus study obtained by iterations morphism, notion coming from combinatorics words. We prove number general theorems provide complete classification case morphisms defined 2 ×