A shorter proof of the distance energy of complete multipartite graphs
Caporossi, Chasser and Furtula in [Les Cahiers du GERAD (2009) G-2009-64] conjectured that the distance energy of a complete multipartite graph of order n with r ≥ 2 parts, each of size at least 2, is equal to 4(n − r). Stevanovic, Milosevic, Hic and Pokorny in [MATCH Commun. Math. Comput. Chem. 70...
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| Format: | Article |
| Language: | English |
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De Gruyter
2017-01-01
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| Series: | Special Matrices |
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| Online Access: | https://doi.org/10.1515/spma-2017-0005 |
| _version_ | 1818676486467485696 |
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| author | So Wasin |
| author_facet | So Wasin |
| author_sort | So Wasin |
| collection | DOAJ |
| description | Caporossi, Chasser and Furtula in [Les Cahiers du GERAD (2009) G-2009-64] conjectured that the distance energy of a complete multipartite graph of order n with r ≥ 2 parts, each of size at least 2, is equal to 4(n − r). Stevanovic, Milosevic, Hic and Pokorny in [MATCH Commun. Math. Comput. Chem. 70 (2013), no. 1, 157-162.] proved the conjecture, and then Zhang in [Linear Algebra Appl. 450 (2014), 108-120.] gave another proof. We give a shorter proof of this conjecture using the interlacing inequalities of a positve semi-definite rank-1 perturbation to a real symmetric matrix. |
| first_indexed | 2024-12-17T08:44:14Z |
| format | Article |
| id | doaj.art-8fbdbc19bf4640c2b6fd3d1d3068a03f |
| institution | Directory Open Access Journal |
| issn | 2300-7451 |
| language | English |
| last_indexed | 2024-12-17T08:44:14Z |
| publishDate | 2017-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj.art-8fbdbc19bf4640c2b6fd3d1d3068a03f2022-12-21T21:56:15ZengDe GruyterSpecial Matrices2300-74512017-01-0151616310.1515/spma-2017-0005spma-2017-0005A shorter proof of the distance energy of complete multipartite graphsSo Wasin0Department of Mathematics and Statistics, San Jose State University, San Jose, CA 95192, United States of AmericaCaporossi, Chasser and Furtula in [Les Cahiers du GERAD (2009) G-2009-64] conjectured that the distance energy of a complete multipartite graph of order n with r ≥ 2 parts, each of size at least 2, is equal to 4(n − r). Stevanovic, Milosevic, Hic and Pokorny in [MATCH Commun. Math. Comput. Chem. 70 (2013), no. 1, 157-162.] proved the conjecture, and then Zhang in [Linear Algebra Appl. 450 (2014), 108-120.] gave another proof. We give a shorter proof of this conjecture using the interlacing inequalities of a positve semi-definite rank-1 perturbation to a real symmetric matrix.https://doi.org/10.1515/spma-2017-0005distance energymultipartite graphinterlacing inequalities05c5015a1805c90 |
| spellingShingle | So Wasin A shorter proof of the distance energy of complete multipartite graphs Special Matrices distance energy multipartite graph interlacing inequalities 05c50 15a18 05c90 |
| title | A shorter proof of the distance energy of complete multipartite graphs |
| title_full | A shorter proof of the distance energy of complete multipartite graphs |
| title_fullStr | A shorter proof of the distance energy of complete multipartite graphs |
| title_full_unstemmed | A shorter proof of the distance energy of complete multipartite graphs |
| title_short | A shorter proof of the distance energy of complete multipartite graphs |
| title_sort | shorter proof of the distance energy of complete multipartite graphs |
| topic | distance energy multipartite graph interlacing inequalities 05c50 15a18 05c90 |
| url | https://doi.org/10.1515/spma-2017-0005 |
| work_keys_str_mv | AT sowasin ashorterproofofthedistanceenergyofcompletemultipartitegraphs AT sowasin shorterproofofthedistanceenergyofcompletemultipartitegraphs |