The clique number of the exact distance t -power graph: Complexity and eigenvalue bounds
Year: 2024
Type: article
Abstract: The exact distance t -power of a graph G , G [ ♯ t ] , is a graph which has the same vertex set as G , with two vertices adjacent in G [ ♯ t ] if and only if they are at distance exactly t in the original graph G . We study the clique number of this graph, also known as the t -equidistant number. We show that it is NP-hard to determine the t -equidistant number of a graph, and that in fact, it is NP-hard to approximate it within a constant factor. We also investigate how the t -equidistant number relates to another distance-based graph parameter; the t -independence number. In particular, we show how large the gap between both parameters can be. The hardness results motivate deriving eigenvalue bounds, which compare well against a known general bound. In addition, the tightness of the proposed eigenvalue bounds is studied.
Source: Discrete Applied Mathematics
Authors: Aida Abiad, Afrouz Jabal Ameli, Luuk Reijnders
Institution: Eindhoven University of Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,860
OpenAlex ID: W4405115389