|
|
- 2016
立方圈的(d,1)-全标号
|
Abstract:
摘要： 一个图G的(d,1)-全标号是V(G)∪E(G)到整数集合的一个映射f, 使得|f(x)-f(y)|≥{1, 若顶点x和y相邻,1, 若边x和y相邻,d, 若顶点x和边y相关联。主要研究了立方圈C3l 的(d,1)-全标号, 得到了d限制条件下立方圈C3l 的(d,1)-全数的确切值。
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
| [1] | HAVET F, YU M L.(<i>p</i>, 1)-total labelling of graphs[J]. Disc Math, 2008, 308:496-513. |
| [2] | SUN Lin, WU Jianliang. On(<i>p</i>, 1)-total labelling of planer graphs[J]. Journal of Combinatorial Optimization, 2015:1-9. |
| [3] | LU Changhong, ZHOU Qing. Path covering number and <i>L</i>(2, 1)-labeling number of graphs[J]. Discrete Applied Mathematics, 2013, 161(13-14):2062-2074. |
| [4] | CHIA M L, KUO D, YAN J H, et al.(<i>p, q</i>)-total labeling of complete graphs[J]. Journal of Combinatorial Optimization, 2013, 25(4):543-561. |
| [5] | WEST D B. Introduction to graph theory[M]. 2 ed. Upper Saddle River: Prentice-Hall, 2001. |
| [6] | BONDY J A, MURTY U S R. Graph theory and its applications[M]. New York: The Macmillan Press, 1976. |
| [7] | ZHU Haiyang, HOU Lifeng, CHEN Wei. The <i>L(p, q)</i>-labelling of planer graphs without 4-cycles[J]. Discrete Applied Mathematics, 2014, 162(1):355-363. |
| [8] | CHEN Dong, WANG Weifan.(2,1)-total labelling of outerplanar graphs[J]. Discrete Applied Mathematics, 2006, 306(12):1217-1231. |
| [9] | SHAO Zhendong, SOLIS-OBA R. <i>L</i>( 2, 1 )- labelings on the modular product of two graphs[J]. Theoretical Computer Science, 2013, 487(2):74-81. |
| [10] | KARST N, OEHRLEIN J, TROXELL D S. The minimum span of <i>L</i>(2,1)-labellings of generalized flowers[J]. Discrete Applied Mathematics, 2015, 181:139-151. |
| [11] | HUANG Yuanzhen, CHIANG Chunying, HUANG Lianghao, et al. On <i>L</i>(2, 1)-labelling of generalized Petersen graphs[J]. Journal of Combinatorial Optimization, 2012, 24(3):266-279. |
