Some Minimal Graphs by Interlacing Eigenvalues

Let G be a simple graph with p vertices and let A(G) be the adjacency matrix of G. The characteristic polynomial of G is the characteristic polynomial of A(G) and roots of the characteristic equation are the eigenvalues of G. In this paper we compute the characteristic polynomial of a class of graph...

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Bibliographic Details
Published in:Electronic notes in discrete mathematics 2003-05, Vol.15, p.216-218
Main Authors: Walikar, H.B., Hamipholi, P.R., Ramane, H.S.
Format: Article
Language:English
Subjects:
AMS Subject classification: 05C50
divisor graphs
eigenvalues
Minimal graphs
Online Access:Get full text
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Summary:Let G be a simple graph with p vertices and let A(G) be the adjacency matrix of G. The characteristic polynomial of G is the characteristic polynomial of A(G) and roots of the characteristic equation are the eigenvalues of G. In this paper we compute the characteristic polynomial of a class of graphs and show that the same class of graphs are minimal. (Here minimal indicates graphs with diameter d and exactly d + 1 different eigenvalues).
ISSN:1571-0653
1571-0653
DOI:10.1016/S1571-0653(04)00587-6