The Wiener index of Sierpiński-like graphs

Sierpiński-like graphs constitute an extensively studied family of graphs of fractal nature applicable in topology, mathematics of the Tower of Hanoi, computer science, and elsewhere. In this paper, we focus on the Wiener polarity index, Wiener index and Harary index of Sierpiński-like graphs. By Sierpiński-like graphs’ special structure and correlation, their Wiener polarity index and some Sierpiński-like graph’s Wiener index and Harary index are obtained.

[1]  Marko Jakovac,et al.  A 2-parametric generalization of Sierpinski gasket graphs , 2014, Ars Comb..

[2]  Andreas M. Hinz,et al.  Coloring Hanoi and Sierpiński graphs , 2012, Discret. Math..

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

[4]  Odile Favaron,et al.  k-Domination and k-Independence in Graphs: A Survey , 2012, Graphs Comb..

[5]  S. Klavžar,et al.  1-perfect codes in Sierpiński graphs , 2002, Bulletin of the Australian Mathematical Society.

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

[7]  Bo Zhou,et al.  On general sum-connectivity index , 2010 .

[8]  Andreas M. Hinz,et al.  The Average Eccentricity of Sierpiński Graphs , 2012, Graphs Comb..

[9]  I. Gutman,et al.  Wiener Index of Trees: Theory and Applications , 2001 .

[10]  A. M. Hinz,et al.  Pascal's triangle and the tower of Hanoi , 1992 .

[11]  Sandi Klavžar,et al.  Edge disjoint cycles through specified vertices , 2005 .

[12]  István Lukovits,et al.  On the Definition of the Hyper-Wiener Index for Cycle-Containing Structures , 1995, J. Chem. Inf. Comput. Sci..

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

[14]  Sandi Klavÿzar,et al.  On distances in Sierpiński graphs: Almost-extreme vertices and metric dimension , 2013 .

[15]  Guojun Li,et al.  Coloring the Square of Sierpiński Graphs , 2015, Graphs Comb..

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

[17]  Yue-Li Wang,et al.  The Hub Number of Sierpiński-Like Graphs , 2011, Theory of Computing Systems.

[18]  Sandi Klavzar,et al.  Vertex-, edge-, and total-colorings of Sierpinski-like graphs , 2009, Discret. Math..

[19]  Guojun Li,et al.  The hamiltonicity and path t-coloring of Sierpiński-like graphs , 2012, Discret. Appl. Math..

[20]  Ivan Gutman,et al.  Graph representation of organic molecules Cayley's plerograms vs. his kenograms , 1998 .

[21]  Pierre Hansen,et al.  Variable neighborhood search for extremal graphs: 1 The AutoGraphiX system , 1997, Discret. Math..

[22]  Bo Zhou,et al.  On a novel connectivity index , 2009 .

[23]  Sylvain Gravier,et al.  Covering codes in Sierpinski graphs , 2010, Discret. Math. Theor. Comput. Sci..

[24]  Ivan Gutman,et al.  A PROPERTY OF THE WIENER NUMBER AND ITS MODIFICATIONS , 1997 .

[25]  Guanghui Wang,et al.  The Linear t-Colorings of Sierpiński-Like Graphs , 2014, Graphs Comb..

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

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

[28]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

[29]  Dezheng Xie,et al.  Equitable L(2, 1)-labelings of Sierpiński graphs , 2010, Australas. J Comb..

[30]  Chunmei Luo,et al.  Metric properties of Sierpiski-like graphs , 2017, Appl. Math. Comput..