Local distance antimagic cromatic number of join product of graphs with cycles or paths

Wai-chee Shiu; Gee-choon Lau; Nalliah M

doi:10.15672/hujms.1266085

Araştırma Makalesi

Local distance antimagic cromatic number of join product of graphs with cycles or paths

Yıl 2024, Cilt: 53 Sayı: 3, 788 - 802, 27.06.2024

Wai-chee Shiu , Gee-choon Lau , Nalliah M

https://doi.org/10.15672/hujms.1266085

Öz

Let $G$ be a graph of order $p$ without isolated vertices. A bijection $f: V \to \{1,2,3,\dots,p\}$ is called a local distance antimagic labeling, if $w_f(u)\ne w_f(v)$ for every edge $uv$ of $G$, where $w_f(u)=\sum_{x\epsilon N(u)} {f(x)}$. The local distance antimagic chromatic number $\chi_{lda}(G)$ is defined to be the minimum number of colors taken over all colorings of $G$ induced by local distance antimagic labelings of $G$. In this paper, we determined the local distance antimagic chromatic number of some cycles, paths, disjoint union of 3-paths. We also determined the local distance antimagic chromatic number of join products of some graphs with cycles or paths.

Anahtar Kelimeler

local distance antimagic chromatic number, join product, cycle, path, null graph

Kaynakça

[1] S. Arumugam, D. Froncek, and N. Kamatchi, Distance magic graphs–A survey, J. Indones. Math. Soc. Special Edition, 1126, 2011.
[2] S. Arumugam and N. Kamatchi, On $(a, d)$-distance antimagic graphs, Australas. J. Combin. 54, 279–287, 2012.
[3] S. Arumugam, K. Premalatha, M. Bača and A. Semaničová-Fecňovčíková, Local antimagic vertex coloring of a graph, Graphs Combin. 33, 275–285, 2017.
[4] J.A. Bondy, U.S.R. Murty, Graph Theory with Applications, New York, MacMillan, 1976.
[5] J. Bensmail, M. Senhaji and K.S. Lyngsie, On a combination of the 1-2-3 conjecture and the antimagic labelling conjecture, Discrete Math. Theor. Comput. Sci. 19 (1), 2017.
[6] T. Divya and S. Devi Yamini, Local distance antimagic vertex coloring of graphs, https://arxiv.org/abs/2106.01833v1, 2021.
[7] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin.1 (Dynamic Surveys),DS6, 2021.
[8] N. Hartsfield and G. Ringel, Pearls in Graph Theory, Academic Press, INC., Boston, 1994.
[9] J. Haslegrave, Proof of a local antimagic conjecture, Discrete Math. Theor. Comput. Sci. 20 (1), 2018.
[10] N. Kamatchi and S. Arumugam, Distance antimagic graphs, J. Combin. Math. Combin. Comput. 84, 6167, 2013.
[11] G.C. Lau, H.K. Ng and W.C. Shiu, Affirmative solutions on local antimagic chromatic number, Graphs Combin. 36, 1337–1354, 2020.
[12] G.C. Lau, W.C. Shiu and H.K. Ng, On local antimagic chromatic number of cyclerelated join graphs, Discuss. Math. Graph Theory, 4 (1), 133–152, 2021.
[13] M. Nalliah, Antimagic labeling of Graphs and digraphs, Ph.D Thesis, Kalasalingam University, Tamil Nadu, India, 2013.
[14] S. Shaebani, On local antimagic chromatic number of graphs, J. Algebr. Syst. 7 (2), 245–256, 2020.
[15] R. Shankar and M. Nalliah, Local vertex antimagic chromatic number of some wheel related graphs, Proyecciones J. Math. 41 (1), 319–334, 2022.
[16] V. Priyadharshini and M. Nalliah, Local distance antimagic chromatic number for the union of complete bipartite graphs, Tamkang J. Math. online, https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4804, 2023.

Yıl 2024, Cilt: 53 Sayı: 3, 788 - 802, 27.06.2024

Wai-chee Shiu , Gee-choon Lau , Nalliah M

https://doi.org/10.15672/hujms.1266085

Öz

Kaynakça

[1] S. Arumugam, D. Froncek, and N. Kamatchi, Distance magic graphs–A survey, J. Indones. Math. Soc. Special Edition, 1126, 2011.
[2] S. Arumugam and N. Kamatchi, On $(a, d)$-distance antimagic graphs, Australas. J. Combin. 54, 279–287, 2012.
[3] S. Arumugam, K. Premalatha, M. Bača and A. Semaničová-Fecňovčíková, Local antimagic vertex coloring of a graph, Graphs Combin. 33, 275–285, 2017.
[4] J.A. Bondy, U.S.R. Murty, Graph Theory with Applications, New York, MacMillan, 1976.
[5] J. Bensmail, M. Senhaji and K.S. Lyngsie, On a combination of the 1-2-3 conjecture and the antimagic labelling conjecture, Discrete Math. Theor. Comput. Sci. 19 (1), 2017.
[6] T. Divya and S. Devi Yamini, Local distance antimagic vertex coloring of graphs, https://arxiv.org/abs/2106.01833v1, 2021.
[7] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin.1 (Dynamic Surveys),DS6, 2021.
[8] N. Hartsfield and G. Ringel, Pearls in Graph Theory, Academic Press, INC., Boston, 1994.
[9] J. Haslegrave, Proof of a local antimagic conjecture, Discrete Math. Theor. Comput. Sci. 20 (1), 2018.
[10] N. Kamatchi and S. Arumugam, Distance antimagic graphs, J. Combin. Math. Combin. Comput. 84, 6167, 2013.
[11] G.C. Lau, H.K. Ng and W.C. Shiu, Affirmative solutions on local antimagic chromatic number, Graphs Combin. 36, 1337–1354, 2020.
[12] G.C. Lau, W.C. Shiu and H.K. Ng, On local antimagic chromatic number of cyclerelated join graphs, Discuss. Math. Graph Theory, 4 (1), 133–152, 2021.
[13] M. Nalliah, Antimagic labeling of Graphs and digraphs, Ph.D Thesis, Kalasalingam University, Tamil Nadu, India, 2013.
[14] S. Shaebani, On local antimagic chromatic number of graphs, J. Algebr. Syst. 7 (2), 245–256, 2020.
[15] R. Shankar and M. Nalliah, Local vertex antimagic chromatic number of some wheel related graphs, Proyecciones J. Math. 41 (1), 319–334, 2022.
[16] V. Priyadharshini and M. Nalliah, Local distance antimagic chromatic number for the union of complete bipartite graphs, Tamkang J. Math. online, https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4804, 2023.

Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Matematik
Yazarlar	Wai-chee Shiu 0000-0002-2819-8480 Gee-choon Lau 0000-0002-9777-6571 Nalliah M 0000-0002-3927-2607
Erken Görünüm Tarihi	14 Nisan 2024
Yayımlanma Tarihi	27 Haziran 2024
Yayımlandığı Sayı	Yıl 2024 Cilt: 53 Sayı: 3

Kaynak Göster

APA	Shiu, W.-c., Lau, G.-c., & M, N. (2024). Local distance antimagic cromatic number of join product of graphs with cycles or paths. Hacettepe Journal of Mathematics and Statistics, 53(3), 788-802. https://doi.org/10.15672/hujms.1266085
AMA	Shiu Wc, Lau Gc, M N. Local distance antimagic cromatic number of join product of graphs with cycles or paths. Hacettepe Journal of Mathematics and Statistics. Haziran 2024;53(3):788-802. doi:10.15672/hujms.1266085
Chicago	Shiu, Wai-chee, Gee-choon Lau, ve Nalliah M. “Local Distance Antimagic Cromatic Number of Join Product of Graphs With Cycles or Paths”. Hacettepe Journal of Mathematics and Statistics 53, sy. 3 (Haziran 2024): 788-802. https://doi.org/10.15672/hujms.1266085.
EndNote	Shiu W-c, Lau G-c, M N (01 Haziran 2024) Local distance antimagic cromatic number of join product of graphs with cycles or paths. Hacettepe Journal of Mathematics and Statistics 53 3 788–802.
IEEE	W.-c. Shiu, G.-c. Lau, ve N. M, “Local distance antimagic cromatic number of join product of graphs with cycles or paths”, Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 3, ss. 788–802, 2024, doi: 10.15672/hujms.1266085.
ISNAD	Shiu, Wai-chee vd. “Local Distance Antimagic Cromatic Number of Join Product of Graphs With Cycles or Paths”. Hacettepe Journal of Mathematics and Statistics 53/3 (Haziran 2024), 788-802. https://doi.org/10.15672/hujms.1266085.
JAMA	Shiu W-c, Lau G-c, M N. Local distance antimagic cromatic number of join product of graphs with cycles or paths. Hacettepe Journal of Mathematics and Statistics. 2024;53:788–802.
MLA	Shiu, Wai-chee vd. “Local Distance Antimagic Cromatic Number of Join Product of Graphs With Cycles or Paths”. Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 3, 2024, ss. 788-02, doi:10.15672/hujms.1266085.
Vancouver	Shiu W-c, Lau G-c, M N. Local distance antimagic cromatic number of join product of graphs with cycles or paths. Hacettepe Journal of Mathematics and Statistics. 2024;53(3):788-802.