Sierpiński graphs S(n,3) are the graphs of the Tower of Hanoi puzzle with n disks, Sierpiński gasket graphs S_n, are the graphs naturally defined by the finite number of iterations that lead to the Sierpiński gasket. An explicit labeling of the vertices of S_n, is introduced. It is proved that S_n is uniquely 3-colorable, that S(n,3) is uniquely 3-edge-colorable, and that chi'(S_n) = 4, thus answering a question from [Australas. J. Combin. 35 (2006) 181-192]. It is also shown that S_n, contains a 1-perfect code only for n = 1 or n = 3 and that every S(n,3) contains a unique Hamiltonian cycle.
COBISS.SI-ID: 14677593
In 2008 our research monograph was published that covers contemporary topics from graph theory. Throughout the book the topics are interrelated via the Cartesian product of graphs. Of course just a part of the book is devoted to the topic of this researh project. More precisely, the Tower of Hanoi graphs are presented as an important example of subgraphs of Cartesian products of complete graphs that are in turn known as Hamming graphs.
COBISS.SI-ID: 14965081