@article{Hayat2024, 
author = {Sakander Hayat and Sunilkumar M. Hosamani and Asad Khan and Ravishankar L. Hutagi and Umesh S. Mujumdar and Mohammed J. F. Alenazi},
title = {A novel edge-weighted matrix of a graph and its spectral properties with potential applications},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {24955-24976},
keywords = {edge weight energy, spectral radius, benzenoid hydrocarbons, structure-property modeling, graphical descriptor},
url = {https://www.sciopen.com/article/10.3934/math.20241216},
doi = {10.3934/math.20241216},
abstract = {Regarding a simple graph  Γ possessing  ν vertices ( ν-vertex graph) and  m edges, the vertex-weight and weight of an edge  e=uv are defined as  w(vi)=dΓ(vi) and  w(e)=dΓ(u)+dΓ(v)−2, where  dΓ(v) is the degree of  v. This paper puts forward a novel graphical matrix named the edge-weighted adjacency matrix (adjacency of the vertices)  Aw(Γ) of a graph  Γ and is defined in such a way that, for any  vi that is adjacent to  vj, its  (i,j)-entry equals  w(e)=dΓ(vi)+dΓ(vj)−2; otherwise, it equals 0. The eigenvalues  λ1w≥λ2w≥…≥λνw of  Aw are called the edge-weighted eigenvalues of  Γ. We investigate the mathematical properties of  Aw(Γ)'s spectral radius  λ1w and energy  Ew(Γ)=∑i=1ν|λiw|. Sharp lower and upper bounds are obtained for  λ1w and  Ew(Γ), and the respective extremal graphs are characterized. Further, we employ these spectral descriptors in structure-property modeling of the physicochemical properties of polycyclic aromatic hydrocarbons for a set of benzenoid hydrocarbons (BHs). Detailed regression analysis showcases that edge-weighted energy outperforms classical adjacency energy in structure-property modeling of the physicochemical properties of BHs.}
}