# A shorter proof of the distance energy of complete multipartite graphs

Special Matrices (2017)

- Volume: 5, Issue: 1, page 61-63
- ISSN: 2300-7451

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topWasin So. "A shorter proof of the distance energy of complete multipartite graphs." Special Matrices 5.1 (2017): 61-63. <http://eudml.org/doc/287973>.

@article{WasinSo2017,

abstract = {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.},

author = {Wasin So},

journal = {Special Matrices},

keywords = {distance energy; multipartite graph; interlacing inequalities},

language = {eng},

number = {1},

pages = {61-63},

title = {A shorter proof of the distance energy of complete multipartite graphs},

url = {http://eudml.org/doc/287973},

volume = {5},

year = {2017},

}

TY - JOUR

AU - Wasin So

TI - A shorter proof of the distance energy of complete multipartite graphs

JO - Special Matrices

PY - 2017

VL - 5

IS - 1

SP - 61

EP - 63

AB - 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.

LA - eng

KW - distance energy; multipartite graph; interlacing inequalities

UR - http://eudml.org/doc/287973

ER -

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