Volume 3, Issue 2
On the Distance Cospectrality of Threshold Graphs

Zhenzhen Lou, Jianfeng Wang & Qiongxiang Huang

CSIAM Trans. Appl. Math., 3 (2022), pp. 335-350.

Published online: 2022-05

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  • Abstract

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].

  • Keywords

Threshold graph, distance matrix, spectrum, characteristic polynomial.

  • AMS Subject Headings

05C50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-3-335, author = {Zhenzhen and Lou and and 23342 and and Zhenzhen Lou and Jianfeng and Wang and and 23343 and and Jianfeng Wang and Qiongxiang and Huang and and 23344 and and Qiongxiang Huang}, title = {On the Distance Cospectrality of Threshold Graphs}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2022}, volume = {3}, number = {2}, pages = {335--350}, abstract = {

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].

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2021-0005}, url = {http://global-sci.org/intro/article_detail/csiam-am/20541.html} }
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].

Zhenzhen Lou, Jianfeng Wang & Qiongxiang Huang. (2022). On the Distance Cospectrality of Threshold Graphs. CSIAM Transactions on Applied Mathematics. 3 (2). 335-350. doi:10.4208/csiam-am.SO-2021-0005
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