A graph is said to be characterized by its permanental spectrum if there is no other non-isomorphic graph with the same permanental spectrum. In this paper, we investigate when a complete bipartite graph Kp,p with some edges deleted is determined by its permanental spectrum. We first prove that a graph obtained from Kp,p by deleting all edges of a star K1,l, provided l < p, is determined by its permanental spectrum. Furthermore, we show that all graphs with a perfect matching obtained from Kp,p by removing five or fewer edges are determined by their permanental spectra.
@article{bwmeta1.element.doi-10_7151_dmgt_1981,
author = {Tingzeng Wu and Heping Zhang},
title = {Per-Spectral Characterizations Of Some Bipartite Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {935-951},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1981}
}
Tingzeng Wu; Heping Zhang. Per-Spectral Characterizations Of Some Bipartite Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 935-951. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1981/