A shorter proof of the distance energy of complete multipartite graphs

Wasin 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 -