Extended Keller Graph and its properties

Abstract

In the paper extended Keller graph Γ³_d is defined and some of its properties, such as Hamiltonian, the independence number, the chromatic number, etc.,are proved. Moreover, the size of a maximum clique of Γ³_d for d = 2, 3, 4 and d ≥ 8 is given and for d = 5, 6, 7 a conjecture is stated.

Mathematics Subject Classification (2010): 05C15, 05C45,05C99.

Keywords: Keller graph, Keller's conjecture