The General Extended Adjacency Eigenvalues of Chain Graphs

Bilal Ahmad Rather, Hilal A. Ganie, Kinkar Chandra Das () and Yilun Shang ()
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Bilal Ahmad Rather: Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain 15551, United Arab Emirates
Hilal A. Ganie: Department of School Education, Jammu and Kashmir Government, Srinagar 193404, Kashmir, India
Kinkar Chandra Das: Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea
Yilun Shang: Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK

Mathematics, 2024, vol. 12, issue 2, 1-16

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.

Keywords: adjacency matrix; graph energy; topological index; chain graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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