2025/02/20 by Dickson Y. B. Annor, Annor, Dickson Y. B.
Computer Science · #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Theory and Algorithms #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.2502.14341
openalex publication_date 2025/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A graph G is a cover of a graph F if there exists an onto mapping π: V(G) → V(F), called a (covering) projection, such that π maps the neighbours of any vertex v in G bijectively onto the neighbours of π(v) in F. This paper is the first attempt to study the connection between domination parameters and graph covers. We focus on the domination number, the total domination number, and the connected domination number. We prove upper and lower bounds for the domination parameters of G. Moreover, we propose a conjecture on the lower bound for the domination number of G and provide evidence to support the conjecture.