The line spectrum of joined complete graphs
Abstract
For a given simple graph G, the line graph ℒ(G) is constructed by associating each vertex of ℒ(G) with an edge of G, and two vertices in ℒ(G) are adjacent if and only if their corresponding edges in G share a common vertex. The line spectrum of a graph refers to the set of eigenvalues of its line graph. In this paper, we determine the line spectrum of graphs derived from complete graphs using the graph operations of join and union. We also compute determinant of various block matrices which stem from the join of multiple complete graphs under line operator.
Fields of Study & Subjects
Graph theory and applications
Matrix Theory and Algorithms
Graph Theory and Algorithms
Publication details
- Journal / source
- Proyecciones (Antofagasta)
- Volume
- 44
- Issue
- 4
- Pages
- 686–701
- Publication date
- 16 February 2026
- Language
- EN