Title: Which graphs are determined by their total numbers of walks?
| Speaker: | Wei Wang |
| Affiliation: | Xi'an Jiaotong University |
| Location: | Please contact Sabrina Lato for the Zoom link. |
Abstract: Walks and closed-walks are ubiquitous in graph theory, which capture lots of important structural information of graphs. In this talk, we shall consider the question in the title. The same question for closed walks is precisely the problem of spectral characterizations of graphs. We show that for most graphs, the number of walks determines the generalized spectrum of graphs and vice versa. Then the above question is equivalent to the problem of generalized spectral characterizations of graphs, a topic which has been studied extensively in recent years. Some simple criterions are provided for graphs G to be determined by their total number of walks, based on some recent results on the generalized spectral characterizations of graphs. Numerical results are also provided to illustrate the effectiveness of the proposed method. This is a joint work with Weifang Lv, Finjin Liu and Wei Wang.