Wheels, Cages and Cubes

Abstract

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, $G_{k}^{p} \approx G;$ and it is said to be k-co-self-complementary if $G_{k}^{p} \approx \bar{G}$. In this paper we characterize the k-self-complementary generalized wheels, cubes and cages.