The smallest positive eigenvalue of graphs /
Sonu Rani
The smallest positive eigenvalue of graphs / Sonu Rani; Guided by Sasmita Barik - Bhubaneswar : IIT Bhubaneswar, 2021. - xxiv, 130p. ; 22 cm.
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.
Eigenvalues
510 / RAN/T
The smallest positive eigenvalue of graphs / Sonu Rani; Guided by Sasmita Barik - Bhubaneswar : IIT Bhubaneswar, 2021. - xxiv, 130p. ; 22 cm.
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.
Eigenvalues
510 / RAN/T