Graphs G and H are called cospectral if they have the same characteristic polynomial. If eigenvalues are integral, then corresponding graphs are called integral graph. In this article we introduce a construction to produce pairs of cospectral integral regular graphs. Generalizing the construction of G4(a, b) and G5(a, b) due to Wang and Sun, we define graphs 𝒢4(G,H) and 𝒢5(G,H) and show that they are cospectral integral regular when G is an integral q-regular graph of order m and H is an integral q-regular graph of order (b − 2)m for some integer b ≥ 3.
@article{bwmeta1.element.doi-10_7151_dmgt_1960,
author = {Ravindra B. Bapat and Masoud Karimi},
title = {Construction of Cospectral Integral Regular Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {595-609},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1960}
}
Ravindra B. Bapat; Masoud Karimi. Construction of Cospectral Integral Regular Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 595-609. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1960/