(d,1)-total labeling of lexicographic products of some classes of graphs

doi:10.3969/j.issn.1000-5641.2019.03.005

Journal of East China Normal University(Natural Sc ›› 2019, Vol. 2019 ›› Issue (3): 35-41.doi: 10.3969/j.issn.1000-5641.2019.03.005

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(d,1)-total labeling of lexicographic products of some classes of graphs

HAN Xin-yin^1,2, YAO Min^1,3, ZUO Lian-cui¹, ZHOU Wei-na¹

1. College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China;
2. Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190, China;
3. College of Mathematical Sciences, East China Normal University, Shanghai 200241, China

Received:2018-04-08 Online:2019-05-25 Published:2019-05-30

Abstract: This paper focuses on (d, 1)-total labeling of the lexicographic products of path P_n and path P_m, path P_n and circle C_n, and gets the exact value of the (d, 1)-total number λ_d^T (G) of lexicographic product P_n·P_m, P_n·C_m under certain constraints.

Key words: lexicographic product, (d, 1)-total labeling, (d, 1)-total number λ_d^T (G)

CLC Number:

O157.5

Cite this article

HAN Xin-yin, YAO Min, ZUO Lian-cui, ZHOU Wei-na. (d,1)-total labeling of lexicographic products of some classes of graphs[J]. Journal of East China Normal University(Natural Sc, 2019, 2019(3): 35-41.

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References

[1] 张焕, 左连翠. 关于图的(d,1)-全标号[J]. 山东大学学报(理学版), 2010, 45(12):1-4.
[2] SZUMNY W, WCH I, WCH A. On the existence and on the number of (k, l)-kernels in the lexicographic product of graphs[J]. Discrete Mathematics, 2008, 308(20):4616-4624.
[3] HAVET F, YU M L. (p, 1)-Total labelling of graphs[J]. Discrete Mathematics, 2008, 308(4):496-513.
[4] 左连翠, 周伟娜. 两类图的(d,1)-全标号[J]. 数学的实践与认识, 2017, 47(9):285-290.
[5] 周伟娜, 左连翠. 几类图的笛卡尔积图的(d,1)-全标号[J]. 山东大学学报(理学版), 2014, 49(4):24-28.

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