Solutions of some 2-distance graph equations
R. Rajkumar, S. Celine Prabha · AIP conference proceedings · 2019
For a finite simple graph X, the 2-distance graph T2(X) of X is the graph having V(X) as its vertex set and two vertices u and v in T2(X) are adjacent if and only if the distance between u and v is exactly 2. A graph G is a 2-distance graph if there exists a graph X such that T2(X) ≅ G. In this paper, we determine all the simple graphs X such that T2(X) ≅ G1 ∪ G2, where G1 and G2 are some classes of graphs.