TY - JOUR T1 - On the Distance Cospectrality of Threshold Graphs AU - Lou , Zhenzhen AU - Wang , Jianfeng AU - Huang , Qiongxiang JO - CSIAM Transactions on Applied Mathematics VL - 2 SP - 335 EP - 350 PY - 2022 DA - 2022/05 SN - 3 DO - http://doi.org/10.4208/csiam-am.SO-2021-0005 UR - https://global-sci.org/intro/article_detail/csiam-am/20541.html KW - Threshold graph, distance matrix, spectrum, characteristic polynomial. AB -

A threshold graph can be represented as the binary sequence. In this paper, we present an explicit formula for computing the distance characteristic polynomial of a threshold graph from its binary sequence, and then give a necessary and sufficient condition to characterize two distance cospectral but non-isomorphic threshold graphs. As its applications, we obtain many families of distance cospectral threshold graphs. This provides a negative answer to the problem posed in [22].