The connected niche graphs of split tournaments

Abstract

 The niche graph of a digraph D has V (D) as the vertex set and an edge uv if and only if (u, w) ∈ A(D) and (v, w) ∈ A(D), or (w, u) ∈ A(D) and (w, v) ∈ A(D) for some w ∈ V (D). In this paper, we find out the characteristics of the connected graph G and the split tournament D = ST(I ∪ K, A) when G is the niche graph of D.