More on Equienergetic Threshold Graphs
Fernando Tura
TL;DR
This paper investigates the energy of threshold graphs, providing infinite sequences of such graphs that share the same energy but differ from the complete graph's energy, addressing a question posed in prior research.
Contribution
It introduces infinite sequences of threshold graphs with equal energy, expanding understanding of graph energy spectra and their variations.
Findings
Identifies infinite threshold graph sequences with identical energy
Shows these sequences differ from the complete graph's energy
Addresses a previously open question in graph energy theory
Abstract
The energy of a graph is defined as the sum the absolute values of the eigenvalues of its adjacency matrix. A threshold graph G on n vertices is coded by a binary sequence of length n. In this paper we answer a question posed by Jacobs et al. [Eigenvalues and energy in threshold graphs, Linear Algebra Appl. 465 (2015) 412-425], by giving an infinite sequences of threshold graphs having the same energy but differ to the complete graph's energy.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGraph theory and applications · Interconnection Networks and Systems · Graph Labeling and Dimension Problems