TY - JOUR
T1 - On spectrum of Sombor matrix and Sombor energy of graphs
AU - Pirzada, Shariefuddin
AU - Rather, Bilal Ahmad
AU - Das, Kinkar Chandra
AU - Shang, Yilun
AU - Gutman, Ivan
PY - 2025/1/13
Y1 - 2025/1/13
N2 - The Sombor index ( SO ) is a recently introduced degree-based graph invariant, defined as the sum over all pairs of adjacent vertices u,v of the term √d2u+d2v , where du and dv denote the degrees of vertices u and v, respectively. The matrix associated with SO is the Sombor matrix, and its spectrum is the Sombor spectrum. In this paper, the connected graphs having exactly two and exactly three Sombor eigenvalues are characterized. Bounds are obtained for the spectral radius and energy of the Sombor matrix, and the corresponding extremal graphs are determined. In addition, the Sombor spectra of several families of graphs are calculated.
AB - The Sombor index ( SO ) is a recently introduced degree-based graph invariant, defined as the sum over all pairs of adjacent vertices u,v of the term √d2u+d2v , where du and dv denote the degrees of vertices u and v, respectively. The matrix associated with SO is the Sombor matrix, and its spectrum is the Sombor spectrum. In this paper, the connected graphs having exactly two and exactly three Sombor eigenvalues are characterized. Bounds are obtained for the spectral radius and energy of the Sombor matrix, and the corresponding extremal graphs are determined. In addition, the Sombor spectra of several families of graphs are calculated.
KW - Sombor index
KW - Sombor matrix
KW - Sombor spectrum
KW - Sombor spectral radius
KW - Sombor energy
UR - http://www.scopus.com/inward/record.url?scp=85215266882&partnerID=8YFLogxK
U2 - 10.1515/gmj-2024-2078
DO - 10.1515/gmj-2024-2078
M3 - Article
SN - 1572-9176
JO - Georgian Mathematical Journal
JF - Georgian Mathematical Journal
ER -