The transformation graph G
L. Z. YI, Baoyindureng Wu · 2009
The transformation graph G ++ − of G is the graph with vertex set V (G)∪ E(G) in which the vertices u and v are joined by an edge if one of the following conditions holds: (i) u, v ∈ V (G) and they are adjacent in G, (ii) u, v ∈ E(G) and they are adjacent in G, (iii) one of u and v is in V (G) while the other is in E(G), and they are not incident in G. In this paper, for a graph G, we determine the independence number of G ++− and give a lower bound for the connectivity of G ++ −. Furthermore, we provide some simple sufficient conditions for G ++ − to be hamiltonian.