The Network Graphs With its Application in Frequency Assignment
Lian Xiang · Journal of Jinling Institute of Technology · 2009
If a graph G has a proper edge coloring which makes the incident edge coloring sets between any two adjacent vertices in graph G are different from each other,such an edge coloring is said to be a quasi-strong edge coloring of graph. The graph with a quasi-strong edge coloring is said to be the network graph(or the quasi-strong edge coloring graph).The minimum chromatic number,which makes the graph G have a quasi-strong edge coloring,is said to be the quasi-strong edge chromatic number of graphs,denoted by χ′qs(G).This paper discusses the classification of network graphs and the enumeration problem of network complete graphs,and gives a network graph conjecture(or quasi-strong edge coloring conjecture): If the connected network graph G has Δ(G)≥2,the quasi-strong edge chromatic number of network graphs has the property thatΔ(G)≤χ′qs(G)≤Δ(G)+3.