Zero forcing is a propagation process on a graph, or digraph, defined in linear algebra to provide a bound for the minimum rank problem. Independently, zero forcing was introduced in physics, computer science and network science, areas where line digraphs are frequently used as models. Zero forcing is also related to power domination, a propagation process that models the monitoring of electric...

This paper describes algorithms for answering shortest path queries in digraphs with small separators and, in particular, in planar digraphs. In this version of the problem, one has to preprocess the input graph so that, given an arbitrary pair of query vertices v and w, the shortest-path distance between v and w can be computed in a short time. The goal is to achieve balance between the prepro...

The semigroup DV of digraphs on a set V of n labeled vertices is defined. It is shown that DV is faithfully represented by the semigroup Bn of n × n Boolean matrices and that the Green’s L, R, H, and D equivalence classifications of digraphs in DV follow directly from the Green’s classifications already established for Bn. The new results found from this are: (i) L, R, and H equivalent digraphs...

The minimum rank of a directed graph Γ is defined to be the smallest possible rank over all real matrices whose ijth entry is nonzero whenever (i, j) is an arc in Γ and is zero otherwise. The symmetric minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i = j) is nonzero whenever {i, j} is an edge in G and is zero o...

1. Introduction. — This paper consists of two related parts. In the first part the theory of D-finite power series in several variables and the theory of symmetric functions are used to prove P-recursiveness for regular graphs and digraphs and related objects, that is, that their counting sequences satisfy linear homogeneous recurrences with polynomial coefficients. Previously this has been acc...

In this paper we present suucient conditions for unweighted digraphs to induce facet-deening inequalities of the linear ordering polytope P n. We introduce constructive operations (Identiication (of nodes),5-Extension) for generating new facets of P n by using already known facets. The identiication generates new digraphs by identiication two nodes of the source di-graph and presented for arbit...

The maximum integer skew-symmetric flow problem (MSFP) generalizes both the maximum flow and maximum matching problems. It was introduced by Tutte [28] in terms of self-conjugate flows in antisymmetrical digraphs. He showed that for these objects there are natural analogs of classical theoretical results on usual network flows, such as the flow decomposition, augmenting path, and max-flow min-c...

We give short proofs of the adjacency matrix characterizations of interval digraphs and unit interval digraphs.

let $d=(v,a)$ be a finite simple directed graph. a function$f:vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (tmdf) if $f(n^-[v])ge 1$ and $f(n^+[v])ge 1$ for eachvertex $vin v$. the twin minus domination number of $d$ is$gamma_{-}^*(d)=min{w(f)mid f mbox{ is a tmdf of } d}$. inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...

Let D = (V,A) be a finite directed graph (digraph) each vertex v ∈ V of which is interpreted as a position and each arc a = (v, v′) ∈ A as a possible move from position v to v′. Two players, 1 and 2, take turns moving a token from a given initial position v0. The game ends as soon as the token returns to a position, where it has already been. By definition, the player who made the last move los...