关键词: 猜想, 对换图的凯莱图, 圈图, 轮图

Abstract: n-cubes are famous interconnection networks.Star graphs，pancake graphs and bubble sort graphs are important interconnection networks designed from Cayley graph model.Cayley graphs of transposition trees are a class of special Cayley graphs.Star graphs and bubble sort graphs are tow kinds Cayley graphs that transposition trees are star and path，respectively.One conjecture of n-cube，star graph，pancake graph，bubble sort graph and Cayley graph of transposition tree is proposed respectively；a conception-Cayley graph of transposition graph is proposed.Furthermore two new classes of networks are developed，called the cycle graphs and the wheel graphs，and the bubble sort graphs and the star graphs embedded in the cycle graphs and the wheel graphs are proved，respectively.

Key words: conjecture, Cayley graph of transposition graph, cycle graph, wheel graph