由Signless Laplacian谱确定的一类奇单圈图

摘要

为了探讨一类奇单圈图的Signless Laplacian谱惟一的的问题,利用图与其线图之间的关系,图与其多项系数之间的关系以及图与其同谱图之间的关系,证明了Signless Laplacian同谱图的一个重要的的结构,即:恰含一个奇单圈图的Signless Laplacian同谱图也是一个连通奇单圈图.在此基础上证明了一类奇单圈图的Signless Laplacian谱惟一性,确定了此类奇单圈图的结构.%To investigate the first-class odd cycle graphs determined by the Signless Laplacian spectrum, the very important structure of Signless Laplacian cospectral graph was proved by using relation between graphs and their line graphs, relation between graphs and polynomial coefficients, and relation between of the graph ahd its cospectral graphs. That is, the Signless Laplacian cospectral graph containing an odd cycle graph is a connected odd cycle graph. On that basis, the uniqueness of Signless Laplacian spectrum of first-class odd cycle graphs was demonstrated, and the structure of this type of odd cycle graphs was determined. It makes the graphs more extensively applied to the research of network reliability and complex network models.