The topological ordering algorithm sorts nodes of a directed graph such that the order of the tail of each arc is lower than the order of its head. In this paper, we introduce the notion of covering between nodes of a directed graph. Then, we apply the topological orderingalgorithm on graphs containing the covering nodes. We show that there exists a cut set withforward arcs in these...

in this paper, we introduce the (g-$psi$) contraction in a metric space by using a graph.let $f,t$ be two multivalued mappings on $x.$ among other things, we obtain a common fixedpoint of the mappings $f,t$ in the metric space $x$ endowed with a graph $g.$

Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$.  Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...

let $g$ be a simple graph with an orientation $sigma$‎, ‎which ‎assigns to each edge a direction so that $g^sigma$ becomes a‎ ‎directed graph‎. ‎$g$ is said to be the underlying graph of the‎ ‎directed graph $g^sigma$‎. ‎in this paper‎, ‎we define a weighted skew‎ ‎adjacency matrix with rand'c weight‎, ‎the skew randi'c matrix ${bf‎ ‎r_s}(g^sigma)$‎, ‎of $g^sigma$ as the real skew symmetric mat...

We introduce a new class of auto-encoders for directed graphs, motivated by direct extension the Weisfeiler-Leman algorithm to pairs node labels. The proposed model learns interpretable latent representations nodes and uses parameterized graph convolutional network (GCN) layers its encoder an asymmetric inner product decoder. Parameters in control weighting exchanged between neighboring nodes. ...

Node representation learning for directed graphs is critically important to facilitate many graph mining tasks. To capture the edges between nodes, existing methods mostly learn two embedding vectors each node, source vector and target vector. However, these separately. For node with very low indegree or outdegree, corresponding cannot be effectively learned. In this paper, we propose a novel D...

We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the n! Hamilton cycles in a complete directed graph on n + 1 vertices corresponds with each of the n! n-permutation matrices P, such that pu,i = 1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n + 1. A graph instance (G) is initially coded as exclusion set ...