JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (02): 22-26.doi: 10.6040/j.issn.1671-9352.0.2014.334

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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.

Key words: general edge-coloring, vertex distinguished by multisets, path, vertex-disjoint union

CLC Number: 

  • O157
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