The General Extended Adjacency Eigenvalues of Chain Graphs

Bilal Ahmad Rather, Hilal Ahmad Ganie, Kinkar Chandra Das, Yilun Shang*

*Corresponding author for this work

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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.
Original languageEnglish
Article number192
Number of pages16
JournalMathematics
Volume12
Issue number2
DOIs
Publication statusPublished - 6 Jan 2024

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