Wheels, Cages and Cubes

Let G = 〈V, E〉 be a graph of order p ≥ 2 and P = {V₁, V₂, … V _k } be a partition of V of order k. The k-complement G _k p of G is obtained as follows: For all V _i and V _j in P, i ≠ j, remove the edges between V _i and V _j , and add the missing edges between them. G is said to be k-self-complementary if for some partition P of V of order k, G _k p ≈ G; and it is said to be k-co-self-complementary if <math display='block'> <mrow> <msubsup> <mi>G</mi> <mi>k</mi> <mi>p</mi> </msubsup> <mo>&#x2248;</mo><mover accent='true'> <mi>G</mi> <mo stretchy='true'>&#x00AF;</mo> </mover> </mrow> </math> $$G_k^p \approx \overline G$$. In this paper we characterize the k-self-complementary generalized wheels, cubes and cages.