Construction of Cospectral Integral Regular Graphs

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...

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Bibliographic Details
Published in:Discussiones Mathematicae Graph Theory
Main Authors: Bapat Ravindra B., Karimi Masoud
Format: Article
Language:English
Published: University of Zielona Góra 2017-08-01
Subjects:
eigenvalue
cospectral graphs
adjacency matrix
integral graphs
05c50
Online Access:https://doi.org/10.7151/dmgt.1960
Description
Summary: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.
ISSN:2083-5892

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