The General Extended Adjacency Eigenvalues of Chain Graphs-Reference-Cited by-同舟云学术

The General Extended Adjacency Eigenvalues of Chain Graphs

Published:2024-01-06 Issue:2 Volume:12 Page:192
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Rather Bilal Ahmad¹^ORCID,Ganie Hilal A.²^ORCID,Das Kinkar Chandra³^ORCID,Shang Yilun⁴^ORCID

Affiliation:

1. Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain 15551, United Arab Emirates

2. Department of School Education, Jammu and Kashmir Government, Srinagar 193404, Kashmir, India

3. Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea

4. Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK

Abstract

In this article, we discuss the spectral properties of the general extended adjacency matrix for chain graphs. In particular, we discuss the eigenvalues of the general extended adjacency matrix of the chain graphs and obtain its general extended adjacency inertia. We obtain bounds for the largest and the smallest general extended adjacency eigenvalues and characterize the extremal graphs. We also obtain a lower bound for the spread of the general extended adjacency matrix. We characterize chain graphs with all the general extended adjacency eigenvalues being simple and chain graphs that are non-singular under the general extended adjacency matrix. Further, we determine the explicit formula for the determinant and the trace of the square of the general extended adjacency matrix of chain graphs. Finally, we discuss the energy of the general extended adjacency matrix and obtain some bounds for it. We characterize the extremal chain graphs attaining these bounds.

Funder

Korean Government

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/12/2/192/pdf

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