Vertex-, edge-, and total-colorings of Sierpinski-like graphs

Vertex-colorings, edge-colorings and total-colorings of the Sierpinski gasket graphs S"n, the Sierpinski graphs S(n,k), graphs S^+(n,k), and graphs S^+^+(n,k) are considered. In particular, @g^''(S"n), @g^'(S(n,k)), @g(S^+(n,k)), @g(S^+^+(n,k)), @g^'(S^+(n,k)), and @g^'(S^+^+(n,k)) are determined.

[1]  S. Lipscomb,et al.  Lipscomb’s () space fractalized in Hilbert’s ²() space , 1992 .

[2]  S. Klavžar,et al.  Hanoi graphs and some classical numbers , 2005 .

[3]  Dan Romik,et al.  Shortest paths in the Tower of Hanoi graph and finite automata , 2003, SIAM J. Discret. Math..

[4]  Alf Jonsson,et al.  A trace theorem for the Dirichlet form on the Sierpinski gasket , 2005 .

[5]  C. N. Campos,et al.  A result on the total colouring of powers of cycles , 2004, Discret. Appl. Math..

[6]  Bojan Mohar,et al.  Crossing numbers of Sierpiński‐like graphs , 2005, J. Graph Theory.

[7]  Anant P. Godbole,et al.  Sierpiński gasket graphs and some of their properties , 2006, Australas. J Comb..

[8]  Daniele Parisse,et al.  On Some Metric Properties of the Sierpinski Graphs S(n, k) , 2009, Ars Comb..

[9]  S. Klavžar,et al.  Graphs S(n, k) and a Variant of the Tower of Hanoi Problem , 1997 .

[10]  Tomaz Pisanski,et al.  Growth in Repeated Truncations of Maps , 2000 .

[11]  S. Lipscomb,et al.  LIPSCOMB'S L(A) SPACE FRACTALIZED IN HILBERT'S I2(A) SPACE , 2010 .

[12]  Daniel Berend,et al.  The diameter of Hanoi graphs , 2006, Inf. Process. Lett..

[13]  Kathryn Fraughnaugh,et al.  Introduction to graph theory , 1973, Mathematical Gazette.

[14]  Sandi Klavzar,et al.  Metric properties of the Tower of Hanoi graphs and Stern's diatomic sequence , 2005, Eur. J. Comb..

[15]  H. Yap.  Total Colourings of Graphs , 1996 .

[16]  A. M. Hinz,et al.  The average distance on the Sierpiński gasket , 1990 .

[17]  S. Klavžar.  Coloring Sierpiński graphs and Sierpiński gasket graphs , 2006 .

[18]  Sandi Klavˇzar.  COLORING SIERPIN´ SKI GRAPHS AND SIERPIN´ SKI GASKET GRAPHS , 2008 .

[19]  C. Smith,et al.  Some Binary Games , 1944, The Mathematical Gazette.

[20]  Sylvain Gravier.  CODES AND $L(2,1)$-LABELINGS IN SIERPI\'NSKI GRAPHS , 2005 .

[21]  Janez Zerovnik,et al.  Behzad-Vizing conjecture and Cartesian-product graphs , 2002, Appl. Math. Lett..

[22]  Vadim A. Kaimanovich,et al.  Random Walks on Sierpiński Graphs: Hyperbolicity and Stochastic Homogenization , 2003 .

[23]  A. M. Hinz,et al.  On the planarity of Hanoi graphs , 2002 .