Year: 2026
Type: preprint
Abstract: Given an integer $k$, deciding whether a graph has a clique of size $k$ is an NP-complete problem. Wilf's inequality provides a spectral lower bound for the clique number of a graph. Strengthening this bound, Elphick and Wocjan proposed a conjecture in 2018 using positive adjacency eigenvalues. In this paper, we present an infinite family of graphs for which the Elphick and Wocjan conjecture is true. We find a stronger spectral lower bound for the clique number for this family of graphs.
Source: arXiv (Cornell University)
Institutions: Indian Institute of Technology Indore, Marshall University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222611900