International Journal of Mathematical Sciences and Computing (IJMSC)
IJMSC Vol. 7, No. 1, 8 Feb. 2021
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Labeling a kind of Cubic Graphs by Subgraph Embedding Method
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Author(s)
Yujie. Bai
1,*
Shufei. Wu
1
Index Terms
Vertex labeling, Friendly labeling, Double-edge blow-up, P2-embedding, C4-embedding.
Abstract
Based on a problem raised by Gao et. al. (Bull. Malays. Math. Sci. Soc., 41 (2018) 443–453.), we construct a family of cubic graphs which are double-edge blow-up of ladder graphs. We determine the full friendly index sets of these cubic graphs by embedding labeling graph method. At the same time, the corresponding labeling graphs are provided.
Cite This Paper
Yujie. Bai, Shufei. Wu," Labeling a kind of Cubic Graphs by Subgraph Embedding Method ", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.7, No.1, pp.1-10, 2021. DOI: 10.5815/ijmsc.2021.01.01
Reference
[1]I. Cahit, Cordial graphs: a weaker version of graceful and harmonious graphs, Ars Combin., 23 (1987) 201–207.
[2]Z. B. Gao, R. Y. Han, S. M. Lee, H. N. Reb, G. C. Lau, A new approach in finding full friendly indices, Bull. Malays. Math. Sci. Soc., 41 (2018) 443–453.
[3]Z. B. Gao, R. Y. Han, S. M. Lee, H. N. Reb, G. C. Lau, Labeling subgraph embeddings and cordiality of Graphs. Iranian Journal of Mathematical Sciences and Informatics., 2 (2019) 79–92.
[4]Z. B. Gao, G. Y. Sun, S. M. Lee, On full friendly index sets of 1-level and 2-levels N-grids, Discrete Appl. Math., 211 (2016) 68–78.
[5]J. F. Hou, H. W. Ma, X. X. Yu and X. Zhang, A bound on judicious of directed graphs, Sci. China Math, 63 (2020) 297–308.
[6]J. F. Hou, and Q. H. Zeng, On a problem of judicious k-Partitions of graphs. J. Graph Theory 85 (2017) 619–643.
[7]M. Hovey, A-cordial graphs, Discrete Math., 93 (1991) 183–194.
[8]H. F. Law, Full friendly index sets of spiders, Ars Combin., 119 (2015) 23–31.
[9]G. Y. Sun, Z. B. Gao, and S. M. Lee, On full friendly index sets of twisted product of M¨ obius ladders, Ars Combin., 128 (2016) 225–239.
[10]W. C. Shiu and M.-H. Ho, Full friendly index sets of slender and flat cylinder graphs, Transactions Combin., 2 (4) (2013) 63–80.
[11]E. Salehi and S. M. Lee, On friendly index sets of trees, Cong. Numer., 178 (2006) 173–183.
[12]W. C. Shiu and S. M. Lee, Full friendly index sets and full product-cordial index sets of twisted cylinders., J. Combin. Number Thoery, 3 (3) (2012) 209–216.
[13]W. C. Shiu and M. H. Ling, Full friendly index sets of Cartesian products of two cycles, Acta Mathematica Sinica, English Series, 26 (2010) 1233–1244.
[14]D. Sinha and J. Kaur, Full friendly index set-I, Discrete Appl. Math., 161(9) (2013) 1262–1274.
[15]D. Sinha and J. Kaur, Full friendly index set-II, J. Combin. Math. Combin. Comput., 79 (2011) 65–75.
[16]W. C. Shiu and H. Kwong, Full friendly index sets of P2× Pn, Discrete Math.,308 (2008) 3688–3693.
[17]W. C. Shiu and F. S. Wong, Full friendly index sets of cylinder graphs, Aus-tralasian J. Combin., 52 (2012) 141–162.
[18]Y. R. Ji and J. M. Liu, On computing the edge-balanced index sets of the circle union graph F (3, n), International Journal of Modern Education and Computer Science (IJMECS)., 8(3) (2016) 22-27.
[19]Y. J. Qin and Y. G. Zheng, On The Edge-balance Index Sets of the Power Circle Nested Graph C_(7^m)×P_(m_7) (m≡2(mod3)), International Journal of Intelligent Systems and Applications(IJISA)., 6(7) (2014) 22-28.