Geodesic
On Generalized Sierpiński Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 547-560.

Voir la notice de l'article provenant de la source Library of Science

In this paper we obtain closed formulae for several parameters of generalized Sierpiński graphs S(G, t) in terms of parameters of the base graph G. In particular, we focus on the chromatic, vertex cover, clique and domination numbers.
Keywords: Sierpiński graphs, vertex cover number, independence number, chromatic number, domination number 
@article{DMGT_2017_37_3_a3,
     author = {Rodr{\'\i}guez-Vel\'azquez, Juan Alberto and Rodr{\'\i}guez-Bazan, Erick David and Estrada-Moreno, Alejandro},
     title = {On {Generalized} {Sierpi\'nski} {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {547--560},
     publisher = {mathdoc},
     volume = {37},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a3/}
}
TY  - JOUR
AU  - Rodríguez-Velázquez, Juan Alberto
AU  - Rodríguez-Bazan, Erick David
AU  - Estrada-Moreno, Alejandro
TI  - On Generalized Sierpiński Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2017
SP  - 547
EP  - 560
VL  - 37
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a3/
LA  - en
ID  - DMGT_2017_37_3_a3
ER  - 
%0 Journal Article
%A Rodríguez-Velázquez, Juan Alberto
%A Rodríguez-Bazan, Erick David
%A Estrada-Moreno, Alejandro
%T On Generalized Sierpiński Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2017
%P 547-560
%V 37
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a3/
%G en
%F DMGT_2017_37_3_a3
Rodríguez-Velázquez, Juan Alberto; Rodríguez-Bazan, Erick David; Estrada-Moreno, Alejandro. On Generalized Sierpiński Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 547-560. http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a3/

[1] D.W. Bange, A.E. Barkauskas and P.J. Slater, Efficient dominating sets in graphs, in: Appl. Discrete Math., R.D. Ringeisen and F.S. Roberts (Ed(s)), (SIAM, Philadelphia, PA, 1988) 189–199.

[2] A. Estrada-Moreno, E.D. Rodríguez-Bazan and J.A. Rodríguez-Velázquez, On the General Randić index of polymeric networks modelled by generalized Sierpiński graphs . arXiv:1510.07982 [math.CO]

[3] R. Frucht and F. Harary, On the corona of two graphs, Aequationes Math. 4 (1970) 322–325. doi:10.1007/BF01844162

[4] T. Gallai, Über extreme Punkt- und Kantenmengen, Ann. Univ. Sci. Budapest Eötvös Sect. Math. 2 (1959) 133–138.

[5] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman & Co., New York, NY, USA, 1979).

[6] J. Geetha and K. Somasundaram, Total coloring of generalized Sierpiński graphs, Australas. J. Combin. 63 (2015) 58–69.

[7] S. Gravier, M. Kovše, M. Mollard, J. Moncel and A. Parreau, New results on variants of covering codes in Sierpiński graphs, Des. Codes Cryptogr. 69 (2013) 181–188. doi:10.1007/s10623-012-9642-1

[8] S. Gravier, M. Kovše and A. Parreau, Generalized Sierpiński graphs, in: Posters at EuroComb’11, Rényi Institute, Budapest, 2011. http://www.renyi.hu/conferences/ec11/posters/parreau.pdf

[9] A.M. Hinz and C.H. auf der Heide, An efficient algorithm to determine all shortest paths in Sierpiński graphs, Discrete Appl. Math. 177 (2014) 111–120. doi:10.1016/j.dam.2014.05.049

[10] A.M. Hinz, S. Klavžar, U. Milutinović and C. Petr, The Tower of Hanoi—Myths and Maths (Birkhäuser/Springer Basel, 2013).

[11] A.M. Hinz, S. Klavžar and S.S. Zemljič, A survey and classification of Sierpińskitype graphs, submitted. http://www.fmf.uni-lj.si/~klavzar/preprints/Ssurvey-submit.pdf

[12] A.M. Hinz and D. Parisse, The average eccentricity of Sierpiński graphs, Graphs Combin. 28 (2012) 671–686. doi:10.1007/s00373-011-1076-4

[13] S. Klavžar and U. Milutinović, Graphs S ( n, k ) and a variant of the Tower of Hanoi problem, Czechoslovak Math. J. 47 (1997) 95–104.

[14] S. Klavžar, U. Milutinović and C. Petr, 1 -perfect codes in Sierpiński graphs, Bull. Aust. Math. Soc. 66 (2002) 369–384. doi:10.1017/S0004972700040235

[15] S. Klavžar, I. Peterin and S.S. Zemljič, Hamming dimension of a graph—The case of Sierpiński graphs, European J. Combin. 34 (2013) 460–473. doi:10.1016/j.ejc.2012.09.006

[16] S. Klavžar and S.S. Zemljič, On distances in Sierpiński graphs: Almost-extreme vertices and metric dimension, Appl. Anal. Discrete Math. 7 (2013) 72–82. doi:10.2298/AADM130109001K

[17] D. Parisse, On some metric properties of the Sierpiński graphs S ( n, k ), Ars Combin. 90 (2009) 145–160.

[18] J.A. Rodríguez-Velázquez and E. Estaji, The strong metric dimension of generalized sierpiński graphs with pendant vertices, Ars Math. Contemp., to appear.

[19] J.A. Rodríguez-Velázquez, J. Tomás-Andreu, On the Randić index of polymeric networks modelled by generalized Sierpiński graphs, MATCH Commun. Math. Comput. Chem. 74 (2015) 145–160.