JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (4): 59-64.doi: 10.6040/j.issn.1671-9352.0.2015.473

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The(d,1)-total labelling of the cube of cycles

BAI Dan, ZUO Lian-cui*   

  1. College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
  • Received:2015-10-09 Online:2016-04-20 Published:2016-04-08

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Abstract: A(d,1)-total labelling of G is an integer-valued function f defined on the set V(G)∪E(G) such that|f(x)-f(y)|≥{1, if vertices x and y are adjacent,1, if edges x and y are adjacent,d, if vertex x and edge y are incident.The(d,1)-total labelling of the cube of cycles are studied, and its(d,1)-total number under the restricted conditions for d is obtained.

Key words: cube of cycles, (d,1)-total number, (d,1)-total labelling

CLC Number: 

  • O157
[1] CHEN Dong, WANG Weifan.(2,1)-total labelling of outerplanar graphs[J]. Discrete Applied Mathematics, 2006, 306(12):1217-1231.
[2] SHAO Zhendong, SOLIS-OBA R. L( 2, 1 )- labelings on the modular product of two graphs[J]. Theoretical Computer Science, 2013, 487(2):74-81.
[3] KARST N, OEHRLEIN J, TROXELL D S. The minimum span of L(2,1)-labellings of generalized flowers[J]. Discrete Applied Mathematics, 2015, 181:139-151.
[4] HUANG Yuanzhen, CHIANG Chunying, HUANG Lianghao, et al. On L(2, 1)-labelling of generalized Petersen graphs[J]. Journal of Combinatorial Optimization, 2012, 24(3):266-279.
[5] LU Changhong, ZHOU Qing. Path covering number and L(2, 1)-labeling number of graphs[J]. Discrete Applied Mathematics, 2013, 161(13-14):2062-2074.
[6] ZHU Haiyang, HOU Lifeng, CHEN Wei. The L(p, q)-labelling of planer graphs without 4-cycles[J]. Discrete Applied Mathematics, 2014, 162(1):355-363.
[7] HAVET F, YU M L.(p, 1)-total labelling of graphs[J]. Disc Math, 2008, 308:496-513.
[8] CHIA M L, KUO D, YAN J H, et al.(p, q)-total labeling of complete graphs[J]. Journal of Combinatorial Optimization, 2013, 25(4):543-561.
[9] SUN Lin, WU Jianliang. On(p, 1)-total labelling of planer graphs[J]. Journal of Combinatorial Optimization, 2015:1-9.
[10] WEST D B. Introduction to graph theory[M]. 2 ed. Upper Saddle River: Prentice-Hall, 2001.
[11] BONDY J A, MURTY U S R. Graph theory and its applications[M]. New York: The Macmillan Press, 1976.
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