The smallest positive eigenvalue of graphs / Sonu Rani; Guided by Sasmita Barik

By:

Sonu Rani [Author]

Contributor(s):

Barik, Sasmita [Guide ]

Material type: Text

TextLanguage: English Publication details: Bhubaneswar : IIT Bhubaneswar, 2021.Description: xxiv, 130p. ; 22 cmSubject(s):

Eigenvalues

DDC classification:

510 RAN/T

Summary: In spectral graph theory, we associate a matrix to the given graph and then study different properties of the graph structure via eigenvalues of this matrix. One of the extensively studied matrices in this regard is the adjacency matrix. Only few of the eigenvalues of this matrix, in particular, the largest, the second largest and the smallest have been studied widely. Let G be a graph simple graph on n vertices and A(G) be the adjacency matrix of G. In this thesis, we focus on the smallest positive eigenvalue of the adjacency matrix. We call the smallest positive eigenvalue of A(G) as the smallest positive eigenvalue of a graph G, and denote it by τ (G). This particular eigenvalue is of importance in topological theory of conjugated π-electron systems.

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Holdings
Item type	Current library	Home library	Call number	Status	Date due	Barcode	Item holds
PhD Thesis	Central Library, IIT Bhubaneswar	Central Library, IIT Bhubaneswar	510 RAN/T (Browse shelf(Opens below))	Not for loan		PHD153

Total holds: 0

Includes bibliographies and index.

In spectral graph theory, we associate a matrix to the given graph and then study different
properties of the graph structure via eigenvalues of this matrix. One of the extensively
studied matrices in this regard is the adjacency matrix. Only few of the eigenvalues of this
matrix, in particular, the largest, the second largest and the smallest have been studied
widely. Let G be a graph simple graph on n vertices and A(G) be the adjacency matrix of
G. In this thesis, we focus on the smallest positive eigenvalue of the adjacency matrix. We
call the smallest positive eigenvalue of A(G) as the smallest positive eigenvalue of a graph
G, and denote it by τ (G). This particular eigenvalue is of importance in topological theory
of conjugated π-electron systems.

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