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.
@article{bwmeta1.element.doi-10_1515_spma-2017-0005,
author = {Wasin So},
title = {A shorter proof of the distance energy of complete multipartite graphs},
journal = {Special Matrices},
volume = {5},
year = {2017},
pages = {61-63},
zbl = {1358.05181},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2017-0005}
}
Wasin So. A shorter proof of the distance energy of complete multipartite graphs. Special Matrices, Tome 5 (2017) pp. 61-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2017-0005/