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

Zhenzhen Lou, Jianfeng Wang & Qiongxiang Huang

DOI: 10.4208/csiam-am.SO-2021-0005

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 = {Lou , ZhenzhenWang , Jianfeng and Huang , Qiongxiang}, 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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