On Directed Graphs with the Same Sum over Arborescence Weights

Abstract

We show that certain digraphs with the same vertex set but different arc sets have the same sum over the weights of all arborescences with a given root vertex. We relate our results to the Matrix-Tree Theorem and show how they provide a graphical approach for factoring matrix determinants.

0

Turn this paper into a full lesson

ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.

Discussion (0)

Sign in to join the discussion.

Loading comments…