Work

Sequence of Bounds for Spectral Radius and Energy of Digraph

Year: 2024

Type: article

Abstract: The graph spectra analyze the structure of the graph using eigenspectra. The spectral graph theory deals with the investigation of graphs in terms of the eigenspectrum. In this paper, the sequence of lower bounds for the spectral radius of digraph D having at least one doubly adjacent vertex in terms of indegree is proposed. Particularly, it is exhibited that ρ(D)≥αj=∑p=1m(χj+1(p))2∑p=1m(χj(p))2, such that equality is attained iff D=G↔+ {DE∉ Cycle}, where each component of associated graph is a k-regular or (k1,k2) semiregular bipartite. By utilizing the sequence of lower bounds of the spectral radius of D, the sequence of upper bounds of energy of D, where the sequence decreases when eU≤αj and increases when eU>αj, are also proposed. All of the obtained inequalities are elaborated using examples. We also discuss the monotonicity of these sequences.

Source: Symmetry

DOI: 10.3390/sym16101386

Authors: Jietong Zhao, Saira Hameed, Uzma Ahmad, Ayesha Tabassum, Leila Asgharsharghi

Institutions: Guangzhou University, University of the Punjab, Government College University, Lahore, University of Bonab

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: National Natural Science Foundation of China