The Strong Edge Colourings of Complete Graphs
Lian Xiang · Journal of Jinling Institute of Technology · 2007
If a graph G has a proper edge colourings such that the incident edge colourings sets between any two vertices in the graph G are different from each other,then such an edge colourings is said to be a strong edge colourings of graph G.The graph with a strong edge colourings is said to be the strong edge colourings graph.The minimum chromatic number to guarantee that the graph G has a strong edge colourings,is said to be the strong edge chromatic number of graph G.This paper uses the strong edge colourings matrix to discuss the strong edge colourings of complete graph and its classification,and proves that when n is odd,the graph Kn is the secondary class strong edge colourings graph and χ′s(Kn)=Δ(Kn)+1;and when n is even,the graph Kn is the third class strong edge colourings graph and χ′s(Kn)=Δ(Kn)+2.Or,χ′s(Kn)=3+2[(n-2)/2],here [x] expresses the maximum integer of ≤x.