Year: 2024
Type: article
Abstract: Let H be a graph of order n with m edges. Let di=d(vi) be the degree of the vertex vi. The extended adjacency matrix Aex(H) of H is an n×n matrix defined as Aex(H)=(bij), where bij=12didj+djdi, whenever vi and vj are adjacent and equal to zero otherwise. The largest eigenvalue of Aex(H) is called the extended adjacency spectral radius of H and the sum of the absolute values of its eigenvalues is called the extended adjacency energy of H. In this paper, we obtain some sharp upper and lower bounds for the extended adjacency spectral radius in terms of different graph parameters and characterize the extremal graphs attaining these bounds. We also obtain some new bounds for the extended adjacency energy of a graph and characterize the extremal graphs attaining these bounds. In both cases, we show our bounds are better than some already known bounds in the literature.
Source: Information
DOI: 10.3390/info15100586
Authors: Alaa Altassan, Hilal A. Ganie, Yilun Shang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,819
OpenAlex ID: W4402863373