A novel method to construct cospectral graphs based on RT operation
Abstract
This paper presents a new graph operation, RT(G), which is formed by transforming each vertex and edge of the original graph G into a triangle. We analyze the relationship between the signless Laplacian characteristic polynomials of the graph RT(G) and various types of characteristic polynomials of graph G, including its adjacency, Laplacian, and signless Laplacian polynomials. Building upon these polynomial relations, we successfully derive a complete characterization of the signless Laplacian spectrum of RT(G). These findings have important applications, especially in the construction of Q − cospectral graphs.
Fields of Study & Subjects
Graph theory and applications
Graph Theory and Algorithms
Matrix Theory and Algorithms
Publication details
- Journal / source
- AIP Advances
- Volume
- 16
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN