Publication Date:
2018-08-25
Description:
Symmetry, Vol. 10, Pages 360: Hyperbolicity on Graph Operators Symmetry doi: 10.3390/sym10090360 Authors: J. A. Méndez-Bermúdez Rosalío Reyes José M. Rodríguez José M. Sigarreta A graph operator is a mapping F : Γ → Γ ′ , where Γ and Γ ′ are families of graphs. The different kinds of graph operators are an important topic in Discrete Mathematics and its applications. The symmetry of this operations allows us to prove inequalities relating the hyperbolicity constants of a graph G and its graph operators: line graph, Λ ( G ) ; subdivision graph, S ( G ) ; total graph, T ( G ) ; and the operators R ( G ) and Q ( G ) . In particular, we get relationships such as δ ( G ) ≤ δ ( R ( G ) ) ≤ δ ( G ) + 1 / 2 , δ ( Λ ( G ) ) ≤ δ ( Q ( G ) ) ≤ δ ( Λ ( G ) ) + 1 / 2 , δ ( S ( G ) ) ≤ 2 δ ( R ( G ) ) ≤ δ ( S ( G ) ) + 1 and δ ( R ( G ) ) − 1 / 2 ≤ δ ( Λ ( G ) ) ≤ 5 δ ( R ( G ) ) + 5 / 2 for every graph which is not a tree. Moreover, we also derive some inequalities for the Gromov product and the Gromov product restricted to vertices.
Electronic ISSN:
2073-8994
Topics:
Mathematics
,
Physics
