A shorter proof of the distance energy of complete multipartite graphs

• Autorzy: Wasin So
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

distance energy; multipartite graph; interlacing inequalities

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 61-63

Daty

wydano

2017-01-01

otrzymano

2016-08-12

zaakceptowano

2016-10-11

online

2017-01-20

Twórcy

autor

Wasin So

• Department of Mathematics and Statistics, San Jose State University, San Jose, CA 95192,,

Identyfikatory

DOI

10.1515/spma-2017-0005