数学与统计学院知识库

本文利用图的量子同态对图的范畴积做了一些研究. 通过将古典同态下的范畴积引入到量子同态下, 得到一类图的范畴积的量子色素数. 同时本文引入量子可乘图的定义并且证明图$K_{2}$ 是量子可乘图, 并给出判断一个图是量子可乘图的充要条件. 作为应用通过图的运算构造一个分离团数和量子团数的图.

In this paper, we use the quantum homomorphism of graph to study the categorical product of graph. By introducing the categorical product of the classical homomorphism into the quantum homomorphism, the quantum chromatic number of the categorical product of a class graphs is obtained. We introduce the concept of quantum multiplicative graph and show that  $K_{2}$   is quantum multiplicative graph. Moreover, we obtain a necessary and sufficient condition that a graph is quantum multiplicative. Finally, we construct graph exhibiting separations between clique number and quantum clique number.