Characterizing graphs of maximum principal ratio
Abstract
The principal ratio of a connected graph, denoted γ(G), is the ratio of the maximum and minimum entries of its first eigenvector. Cioaba and Gregory conjectured that the graph on n vertices maximizing γ(G) is a kite graph: a complete graph with a pendant path. In this paper we prove their conjecture.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.