General edge-coloring of mPn which is vertex distinguished by multisets

GUO Hong-yuan1, CHEN Xiang-en1, WANG Zhi-wen2

1. 1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China;
2. College of Mathematics and Computer, Ningxia University, Yinchuan 750021, Ningxia, China
• Received:2014-07-15 Revised:2014-11-13 Online:2015-02-20 Published:2015-01-27

Abstract: Let G be a simple graph. A general edge-coloring of a graph G is an assignment of a number of colors to the edges. It is not necessary to assign two distinct colors to two adjacent edges. A general edge-coloring f of a graph G is called vertex distinguished by multisets, if, for any two distinct vertices u,v of a graph G, the multiset of the colors used to color the edges incident with u is different from the multiset of the colors used to color the edges incident with v. The minimum number of colors required for a general edge-coloring of G which is vertex distinguishing by multisets, denoted by c(G), is called the vertex distinguishing general edge chromatic number of G by multisets. Suppose mPn denotes the vertex-disjoint union of m paths of length n. The vertex distinguishing general edge-coloring(by multisets) of mPn will be discussed.

CLC Number:

• O157
 [1] AIGNER M, TRIESCH E. Irregular assignments and two problems ála Ringel[C]// Bodendiek and Henn, eds. Topics in Combinatorics and Graph Theory. Oberwolfach: Physica-Verlag HD, 1990: 29-36. [2] WITTMANN P. Vertex-distinguishing edge-colorings of 2-regular graphs[J]. Discrete Applied Mathematics, 1997, 79:265-277. [3] AIGNER M, TRIESCH E, TUZA Z. Irregular assignments and vertex-distinguishing edge-colorings of graphs[C]// Combinatorics'90, Annals of Discrete Mathematics, [S.l.]: North-Holland,1992, 52:1-9. [4] BURRIS A C. The irregular coloring number of a tree[J]. Discrete Mathematics, 1995, 141:279-283.
 [1] WANG Feng, MAN Yuan, WANG Xing-le. N-shortest paths retrieval algorithm based on artificial immunity [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(9): 35-40. [2] WANG De-ping, FAN Wen-yi, WEN Qian, FAN Ting-jun. Cytotoxicity of ofloxacin to human corneal epithelial cells and its cellular and molecular mechanisms [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 11-17. [3] YI Wen-hui, WANG Yan-ping, WANG Hua-tian, MA Xue-song, WANG Wen-bo. Influences of phenolic acids on soil nitrification in poplar plantation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(1): 27-35. [4] DENG Li-hua, DENG Yu-ping, Louis W. Shapiro. The Riordan group and symmetric lattice paths [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 82-89. [5] GUO JI-wei, JIN Dan. Degradation of co-activator Yki of the hippo pathway through ubiquitinationby Slimb [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(01): 37-41. [6] WANG Hua-tian, WANG Yan-ping*. Hotspot discussion on decline mechanism of replanted plantation [J]. J4, 2013, 48(7): 1-8. [7] QIU Xiu-feng1,2, LIU Jian-wei1, WU Qian-hong1, LIU Jian-hua1. Multipath interdomain routing decision verification protocol [J]. J4, 2013, 48(7): 39-45. [8] GUO Xiao-dong， JIAO Liang， QIU Yi-hong， GE Lian-sheng. Design and implementation of a multi-path inter-domain routing simulator based on Click and NS2 [J]. J4, 2013, 48(11): 36-43. [9] SONG Bao-yang, WANG Xiao-zong, REN Yu-ping. Properly colored paths and cycles in edge colored graphs [J]. J4, 2012, 47(6): 63-66. [10] SUN Yi1, SU Gui-fu2. An identity in terms of 2-Motzkin paths and its applications [J]. J4, 2012, 47(6): 90-94. [11] ZHANG Shi-liang1, LI Yu-ying1,2, LIN Hong-kang1,2. Half P-sets (XF, X) and path match of navigation data [J]. J4, 2012, 47(1): 116-120. [12] JIANG Hua, LI Ming-zhen, WANG Xin. A  PPM probabilistic packet marking improving scheme [J]. J4, 2011, 46(9): 85-88. [13] LUO Jin-mei, ZUO Lian-cui*. On the island sequences of L(2,1)-labeling of graphs [J]. J4, 2011, 46(6): 49-52. [14] JU Ying-lin, LI Xiao-ming*. Allelopathic effects of three submerged macrophytes in the Nansi Lake on Microcystis aeruginosa [J]. J4, 2011, 46(3): 1-8. [15] WANG Guo-xing. Vertex distinguishing IE-total chromatic numbers of mC3 [J]. J4, 2011, 46(2): 57-61.
Viewed
Full text

Abstract

Cited

Shared
Discussed