奇异同谱图的构造

Construction of singularly cospectral graphs

2个图称为奇异同谱的,如果它们有相同的非零奇异值及重数。奇异同谱较同谱弱,但比等能量强。利用t-联(阴影)冠图图运算及分块矩阵技巧,构造一类新的奇异同谱图,对研究等能量图的结构及图谱性质具有重要意义。

Two graphs are called singularly cospectral if they have the same nonzero singular value with the same multiplicity.Singularly cospectral is weaker than cospectral but stronger than equienergetic.A new construction of singularly cospectral graph is derived using the operation of t-join(shadow)corona of a graph and the technique of block matrix which has great significance for studying the structural and spectral properties of equienergetic graphs.