On the vertex-distinguishing proper edge coloring of composition of complete graph and star

  • Authors:

  • Fang Yang;Xiang-En Chen;Chunyan Ma

  • Affiliations:

  • -;-;-

  • Venue:
  • Information Processing Letters
  • Year:
  • 2014

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Abstract

A proper k-edge coloring of a simple graph G is called k-vertex-distinguishing proper edge coloring (k-VDPEC) if for any two distinct vertices u and v of G, the set of colors assigned to edges incident to u differs from the set of colors assigned to edges incident to v. The minimum number of colors required for a vertex-distinguishing proper edge coloring of G, denoted by @g"s^'(G), is called the vertex-distinguishing proper edge chromatic number. For p=2 and q=4, we will obtain vertex-distinguishing proper edge chromatic number of composition of complete graph K"p with order p and star S"q with order q, which is pq.