<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

Published Online: May 17, 2018

Page range: 303 - 308

Received: Jan 27, 2018

Accepted: Mar 16, 2018

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

Keywords
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

Published Online: May 17, 2018

Page range: 303 - 308

Received: Jan 27, 2018

Accepted: Mar 16, 2018

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

Keywordsgraph, complement, pendent path, adjacency matrix, the least eigenvalue

© 2018

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

Keywords
graph, complement, pendent path, adjacency matrix, the least eigenvalue