Rank of weighted digraphs with blocks

by   Ranveer Singh, et al.

Let G be a digraph and r(G) be its rank. Many interesting results on the rank of an undirected graph appear in the literature, but not much information about the rank of a digraph is available. In this article, we study the rank of a digraph using the ranks of its blocks. In particular, we define classes of digraphs, namely r_2-digraph, and r_0-digraph, for which the rank can be exactly determined in terms of the ranks of subdigraphs of the blocks. Furthermore, the rank of directed trees, simple biblock graphs, and some simple block graphs are studied.


page 1

page 2

page 3

page 4


Nonsingular Block Graphs: An Open Problem

A block graph is a graph in which every block is a complete graph (cliqu...

Nonsingular (Vertex-Weighted) Block Graphs

A graph G is nonsingular (singular) if its adjacency matrix A(G) is nons...

Spectral Rank Monotonicity on Undirected Networks

We study the problem of score and rank monotonicity for spectral ranking...

Minimal Rank Completions for Overlapping Blocks

We consider the multi-objective optimization problem of choosing the bot...

Monotonicity in Undirected Networks

Is it always beneficial to create a new relationship (have a new followe...

A note on spanoid rank

We construct a spanoid S on n elements with rank(S) > n^c f-rank(S) wher...

Stable Set Polytopes with High Lift-and-Project Ranks for the Lovász-Schrijver SDP Operator

We study the lift-and-project rank of the stable set polytopes of graphs...

Please sign up or login with your details

Forgot password? Click here to reset