On a multiplicative graph function conjecture

  title={On a multiplicative graph function conjecture},
  author={Lih-Hsing Hsu},
  journal={Discrete Mathematics},
For any graph H, the function h,. defined by setting h,(G) equal to the number of homomorphisms from G into H, is a multiplicative increasing function. L.ov&sz [2] has asked whether ail nonzero multiplicative increasing functions are generated by functions of this type. We show that this is not the case. I-iowever, the classification of multiplicative increasing aaph fUllCtionS iS Still unsolved. we prove several properties of such functions in this pqK?r.