<abstract xmlns="http://www.w3.org/1999/xhtml"> The adjacency matrix of a graph is a matrix which represents adjacent relation between the vertices of the graph. Its minimum eigenvalue is defined as the least eigenvalue of the graph. Let Gn be the set of the graphs of order n, whose complements are connected and have pendent paths. This paper investigates the least eigenvalue of the graphs and characterizes the unique graph which has the minimum least eigenvalue in Gn.</abstract>

The adjacency matrix of a graph is a matrix which represents adjacent relation between the vertices of the graph. Its minimum eigenvalue is defined as the least eigenvalue of the graph. Let Gn be the set of the graphs of order n, whose complements are connected and have pendent paths. This paper investigates the least eigenvalue of the graphs and characterizes the unique graph which has the minimum least eigenvalue in Gn.

The Least Eigenvalue of the Graphs Whose Complements Are Connected and Have Pendent Paths

Journal of Artificial Intelligence and Soft Computing Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The adjacency matrix of a graph is a matrix which represents adjacent relation between the vertices of the graph. Its minimum eigenvalue is defined as the...

The Least Eigenvalue of the Graphs Whose Complements Are Connected and Have Pendent Paths

Publié en ligne: 17 mai 2018

Pages: 303 - 308

Reçu: 27 janv. 2018

Accepté: 16 mars 2018

DOI: https://doi.org/10.1515/jaiscr-2018-0020

Mots clés
graph, complement, pendent path, adjacency matrix, the least eigenvalue

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The Least Eigenvalue of the Graphs Whose Complements Are Connected and Have Pendent Paths

Publié en ligne: 17 mai 2018

Pages: 303 - 308

Reçu: 27 janv. 2018

Accepté: 16 mars 2018

DOI: https://doi.org/10.1515/jaiscr-2018-0020

Mots clésgraph, complement, pendent path, adjacency matrix, the least eigenvalue

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
graph, complement, pendent path, adjacency matrix, the least eigenvalue