BibTex RIS Kaynak Göster

Regular handicap tournaments of high degree

Yıl 2016, Cilt: 3 Sayı: 3, 159 - 164, 09.08.2016
https://doi.org/10.13069/jacodesmath.22530

Öz

A  handicap distance antimagic labeling of a graph $G=(V,E)$ with $n$ vertices is a bijection ${f}: V\to \{ 1,2,\ldots ,n\} $ with the property that ${f}(x_i)=i$ and the sequence of the weights $w(x_1),w(x_2),\ldots,w(x_n)$
(where $w(x_i)=\sum\limits_{x_j\in N(x_i)}f(x_j)$)
forms an increasing arithmetic progression with difference one. A graph $G$ is a {\em handicap distance antimagic graph} if it allows a handicap distance antimagic labeling.
We construct $(n-7)$-regular handicap distance antimagic graphs for every order $n\equiv2\pmod4$ with a few small exceptions. This result complements results by Kov\'a\v{r}, Kov\'a\v{r}ov\'a, and Krajc~[P. Kov\'a\v{r}, T. Kov\'a\v{r}ov\'a, B. Krajc, On handicap labeling of regular graphs, manuscript, personal communication, 2016] who found such graphs with regularities smaller than $n-7$.

Kaynakça

  • S. Arumugam, D. Froncek, N. Kamatchi, Distance magic graphs – a survey, J. Indones. Math. Soc. Special Edition (2011) 1–9.
  • G. Chartrand, L. Lesniak, Graphs and Digraphs, Chapman and Hall, CRC, Fourth edition, 2005.
  • D. Froncek, Fair incomplete tournaments with odd number of teams and large number of games, Congr. Numer. 187 (2007) 83–89.
  • D. Froncek, Handicap distance antimagic graphs and incomplete tournaments, AKCE Int. J. Graphs Comb. 10(2) (2013) 119–127.
  • D. Froncek, Handicap incomplete tournaments and ordered distance antimagic graphs, Congr. Numer. 217 (2013) 93–99.
  • D. Froncek, P. Kovár, T. Kovárová, Fair incomplete tournaments, Bull. Inst. Combin. Appl. 48 (2006) 31–33.
  • J. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 5 (# DS6) (2015) 43 pp.
  • T. Harmuth, Ueber magische Quadrate und ähnliche Zahlenfiguren, Arch. Math. Phys. 66 (1881) 286–313.
  • T. Harmuth, Ueber magische Rechtecke mit ungeraden Seitenzahlen, Arch. Math. Phys. 66 (1881) 413–447.
  • M. Miller, C. Rodger, R. Simanjuntak, Distance magic labelings of graphs, Australas. J. Combin. 28 (2003) 305–315.
  • K. A. Sugeng, D. Froncek, M. Miller, J. Ryan, J. Walker, On distance magic labeling of graphs, J. Combin. Math. Combin. Comput. 71 (2009) 39–48.
  • V. Vilfred, $sum$-labelled graph and circulant graphs, Ph.D. Thesis, University of Kerala, Trivandrum, India, 1994.
Yıl 2016, Cilt: 3 Sayı: 3, 159 - 164, 09.08.2016
https://doi.org/10.13069/jacodesmath.22530

Öz

Kaynakça

  • S. Arumugam, D. Froncek, N. Kamatchi, Distance magic graphs – a survey, J. Indones. Math. Soc. Special Edition (2011) 1–9.
  • G. Chartrand, L. Lesniak, Graphs and Digraphs, Chapman and Hall, CRC, Fourth edition, 2005.
  • D. Froncek, Fair incomplete tournaments with odd number of teams and large number of games, Congr. Numer. 187 (2007) 83–89.
  • D. Froncek, Handicap distance antimagic graphs and incomplete tournaments, AKCE Int. J. Graphs Comb. 10(2) (2013) 119–127.
  • D. Froncek, Handicap incomplete tournaments and ordered distance antimagic graphs, Congr. Numer. 217 (2013) 93–99.
  • D. Froncek, P. Kovár, T. Kovárová, Fair incomplete tournaments, Bull. Inst. Combin. Appl. 48 (2006) 31–33.
  • J. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 5 (# DS6) (2015) 43 pp.
  • T. Harmuth, Ueber magische Quadrate und ähnliche Zahlenfiguren, Arch. Math. Phys. 66 (1881) 286–313.
  • T. Harmuth, Ueber magische Rechtecke mit ungeraden Seitenzahlen, Arch. Math. Phys. 66 (1881) 413–447.
  • M. Miller, C. Rodger, R. Simanjuntak, Distance magic labelings of graphs, Australas. J. Combin. 28 (2003) 305–315.
  • K. A. Sugeng, D. Froncek, M. Miller, J. Ryan, J. Walker, On distance magic labeling of graphs, J. Combin. Math. Combin. Comput. 71 (2009) 39–48.
  • V. Vilfred, $sum$-labelled graph and circulant graphs, Ph.D. Thesis, University of Kerala, Trivandrum, India, 1994.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Bölüm Makaleler
Yazarlar

Dalibor Froncek

Aaron Shepanik Bu kişi benim

Yayımlanma Tarihi 9 Ağustos 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 3 Sayı: 3

Kaynak Göster

APA Froncek, D., & Shepanik, A. (2016). Regular handicap tournaments of high degree. Journal of Algebra Combinatorics Discrete Structures and Applications, 3(3), 159-164. https://doi.org/10.13069/jacodesmath.22530
AMA Froncek D, Shepanik A. Regular handicap tournaments of high degree. Journal of Algebra Combinatorics Discrete Structures and Applications. Ağustos 2016;3(3):159-164. doi:10.13069/jacodesmath.22530
Chicago Froncek, Dalibor, ve Aaron Shepanik. “Regular Handicap Tournaments of High Degree”. Journal of Algebra Combinatorics Discrete Structures and Applications 3, sy. 3 (Ağustos 2016): 159-64. https://doi.org/10.13069/jacodesmath.22530.
EndNote Froncek D, Shepanik A (01 Ağustos 2016) Regular handicap tournaments of high degree. Journal of Algebra Combinatorics Discrete Structures and Applications 3 3 159–164.
IEEE D. Froncek ve A. Shepanik, “Regular handicap tournaments of high degree”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 3, sy. 3, ss. 159–164, 2016, doi: 10.13069/jacodesmath.22530.
ISNAD Froncek, Dalibor - Shepanik, Aaron. “Regular Handicap Tournaments of High Degree”. Journal of Algebra Combinatorics Discrete Structures and Applications 3/3 (Ağustos 2016), 159-164. https://doi.org/10.13069/jacodesmath.22530.
JAMA Froncek D, Shepanik A. Regular handicap tournaments of high degree. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3:159–164.
MLA Froncek, Dalibor ve Aaron Shepanik. “Regular Handicap Tournaments of High Degree”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 3, sy. 3, 2016, ss. 159-64, doi:10.13069/jacodesmath.22530.
Vancouver Froncek D, Shepanik A. Regular handicap tournaments of high degree. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3(3):159-64.