Oriented spanning trees and stationary distribution of digraphs

نویسندگان

چکیده

By using biclique partitions of digraphs, this paper gives reduction formulas for the number oriented spanning trees, stationary distribution vector and Kemeny's constant digraphs. As applications, we give a method enumerating trees undirected graphs by vertex degrees partitions. The partition formula also extends results Knuth Levine from line digraphs to general

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Oriented trees in digraphs

Let f(k) be the smallest integer such that every f(k)-chromatic digraph contains every oriented tree of order k. Burr proved f(k) ≤ (k − 1)2 in general, and conjectured f(k) = 2k − 2. Burr also proved that every (8k − 9)-chromatic digraph contains every antidirected tree. We improve both of Burr’s bounds. We show that f(k) ≤ k2/2 − k/2 + 1 and that every antidirected tree of order k is containe...

متن کامل

Independent Spanning Trees with Small Depths in Iterated Line Digraphs

We show that the independent spanning tree conjecture on digraphs is true if we restrict ourselves to line digraphs. Also, we construct independent spanning trees with small depths in iterated line digraphs. From the results, we can obtain independent spanning trees with small depths in de Bruijn and Kautz digraphs that improve the previously known upper bounds on the depths.

متن کامل

Diameter and Stationary Distribution of Random $r$-out Digraphs

Let D(n, r) be a random r-out regular directed multigraph on the set of vertices {1, . . . , n}. In this work, we establish that for every r ≥ 2, there exists ηr > 0 such that diam(D(n, r)) = (1 + ηr + o(1)) logr n. Our techniques also allow us to bound some extremal quantities related to the stationary distribution of a simple random walk on D(n, r). In particular, we determine the asymptotic ...

متن کامل

Optimal Self-healing of Smart Distribution Grids Based on Spanning Trees to Improve System Reliability

In this paper, a self-healing approach for smart distribution network is presented based on Graph theory and cut sets. In the proposed Graph theory based approach, the upstream grid and all the existing microgrids are modeled as a common node after fault occurrence. Thereafter, the maneuvering lines which are in the cut sets are selected as the recovery path for alternatives networks by making ...

متن کامل

Spanning galaxies in digraphs

A star is an arborescence in which the root dominates all the other vertices. A galaxy is a vertex-disjoint union of stars. The directed star arboricity of a digraph D, denoted by dst(D), is the minimum number of galaxies needed to cover A(D). In this paper, we show that dst(D) ≤ Δ(D) + 1 and that if D is acyclic then dst(D) ≤ Δ(D). These results are proved by considering the existence of spann...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Advances in Applied Mathematics

سال: 2023

ISSN: ['1090-2074', '0196-8858']

DOI: https://doi.org/10.1016/j.aam.2023.102576