几类冠图的邻强边色数

Adjacent Strong Edge Chromatic Number of Some Corona Graphs

图的强染色来自计算机科学,有着很强的实际背景,但确定图的强色数是非常困难的。张忠辅,刘林忠,王建方等研究了图的邻强边染色,并提出了邻强边染色猜想:对任意连通图G G,|V|≥3且G≠C5有Δ≤χa′s(G)≤Δ+2。研究了树、圈、扇、轮、完全二部图及完全图的冠图的邻强边色数;证明了:Δ≤χa′s(G)≤Δ+1,且χa′s(G)≤Δ+1当且仅当G[VΔ]≠Φ。

The strong edge coloring of graphs comes from computer science and has a very strong practical background, but it is very difficult to determine its strong chromatic number for any graphs. Zhang Zhongfu, Liu Linzhong, Wang Jianfang et al. have studied the adjacent strong edge coloring of graphs and put forward the adjacent strong edge coloring conjecture： for any connected graph G, ｜ V ｜ ≥3 and G≠ C5, there is △≤X＇as（ G）≤△ ＋ 2. This paper studied the adjacent strong edge chromatic numbers of the corona graphs with trees, cycles, fans, wheels, complete bipartite graphs, complete graphs, and proved：△≤X＇as （G）≤△ ＋1, and X＇as（G）≤△ ＋1 iff G[V△]≠Ф.