Produtos de Grafos Z_m-bem-cobertos

Authors

  • Márcia Rodrigues Cappelle Santana UFG - Universidade Federal de Goiás
  • Rommel Melgaço Barbosa UFG - Universidade Federal de Goiás

DOI:

https://doi.org/10.5540/tema.2012.013.01.0075

Abstract

Um grafo é $Z_m$-bem-coberto se $|I| \equiv |J|$ (mod m), $m\geq 2,$ para todo $I$, $J$ conjuntos independentes maximais em $V(G)$. Um grafo $G$ é fortemente $Z_m$-bem-coberto se $G$ é um grafo $Z_m$-bem-coberto e $G\backslash \{e\}$ é $Z_m$-bem-coberto, $\forall e \in E(G)$. Um grafo $G$ é $1$-$Z_m$-bem-coberto se $G$ é $Z_m$-bem-coberto e $G\backslash \{v\}$ é $Z_m$-bem-coberto, $\forall v \in V(G)$. Mostramos que os grafos $1$-$Z_m$-bem-cobertos, bem como os fortemente $Z_m$-bem-cobertos, com exceção de $K_1$ e $K_2$, têm cintura $ \leq 5$. Mostramos uma condição necessária e suficiente para que produtos lexicográficos de grafos sejam $Z_m$-bem-cobertos e algumas propriedades para o produto cartesiano de ciclos.

Author Biographies

Márcia Rodrigues Cappelle Santana, UFG - Universidade Federal de Goiás

Instituto de Informática

Rommel Melgaço Barbosa, UFG - Universidade Federal de Goiás

Doutor em Computação pela UFRJ, 1999.

Professor no INF/UFG.

References

M. Asté, F. Havet, C.L. Sales, Grundy number and products of graphs, Discrete Mathematics, 310 (2010), 1482–1490.

R.M. Barbosa, On 1-Zm-well-covered graphs and strongly Zm-well-covered graphs, Ars Combinatoria, 57 (2000), 225–232.

R.M. Barbosa, “Sobre Conjuntos Independentes Maximais em Grafos”, Tese de Doutorado, COPPE-UFRJ, 1999.

R.M. Barbosa, M.N. Ellingham, A characterisation of cubic parity graphs, Australasian Journal of Combinatorics, 28 (2003), 273–293.

R.M. Barbosa, B. Hartnell, Almost parity graphs and claw-free parity graphs, J. Combin. Math. Combin. Comput., 27 (1998), 117–122.

R.M. Barbosa, B. Hartnell, Characterization of Zm-well-covered graphs for some classes of graphs, Discrete Mathematics, 233 (2001), 293–297.

J.A. Bondy, U.S.R. Murty, “Graph Theory”, Graduate Texts in Mathematics, Springer, 2008.

Y. Caro, Subdivisions, parity and well-covered graphs, J. Graph Theory, 25 (1997), 85–94.

Y. Caro, M. Ellingham, J. Ramey, Local structure when all maximal independent sets have equal weight, SIAM J. Discrete Mathematics, 11 (1998), 644–654.

Y. Caro, B. Hartnell, A Characterization of Zm-well-covered graphs of girth 6 or more, J. Graph Theory, 33 (2000), 246–255.

A.O. Fradkin, On the well-coveredness of Cartesian products of graphs, Discrete Mathematics, 309 (2009), 238–246.

R. Hammack, W. Imrich, S. Klavzar “Handbook of Product Graphs”, Second Edition, CRC Press, 2011.

B. Hartnell, Well-covered graphs, J. Combin. Math. Combin. Comput., 29 (1999), 107–115.

R.M. Karp, Reducibility among combinatorial problems, em “Complexity of Computer Computations” (Yorktown Heights), pp. 85-104, Nova York, 1972.

R.J. Nowakowski, K. Seyffarth, Small cycle double covers of products I: Lexicographic product with paths and cycles, J. Graph Theory, 57 (2008), 99–123.

M.R. Pinter, Strongly well-covered graphs, Discrete Mathematics, 132 (1994), 231–246.

J. Topp, L. Volkmann, On the well coveredness of Products of Graphs, Ars Combinatoria, 33 (1992), 199–215.

Downloads

Published

2012-03-17

How to Cite

Santana, M. R. C., & Barbosa, R. M. (2012). Produtos de Grafos Z_m-bem-cobertos. Trends in Computational and Applied Mathematics, 13(1), 75–83. https://doi.org/10.5540/tema.2012.013.01.0075

Issue

Vol. 13 No. 1 (2012)

Section

Original Article

License

Authors who publish in this journal agree to the following terms: 

  1. Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.

  2. Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
     

  3. Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).

  4. This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
    author. This is in accordance with the BOAI definition of open access

 

Intellectual Property

All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.