# Construction of Cospectral Integral Regular Graphs

• Volume: 37, Issue: 3, page 595-609
• ISSN: 2083-5892

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## Abstract

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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.

## How to cite

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Ravindra B. Bapat, and Masoud Karimi. "Construction of Cospectral Integral Regular Graphs." Discussiones Mathematicae Graph Theory 37.3 (2017): 595-609. <http://eudml.org/doc/288315>.

@article{RavindraB2017,
abstract = {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.},
author = {Ravindra B. Bapat, Masoud Karimi},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {eigenvalue; cospectral graphs; adjacency matrix; integral graphs},
language = {eng},
number = {3},
pages = {595-609},
title = {Construction of Cospectral Integral Regular Graphs},
url = {http://eudml.org/doc/288315},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Ravindra B. Bapat
AU - Masoud Karimi
TI - Construction of Cospectral Integral Regular Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 3
SP - 595
EP - 609
AB - 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.
LA - eng
KW - eigenvalue; cospectral graphs; adjacency matrix; integral graphs
UR - http://eudml.org/doc/288315
ER -

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