Graphs can be used to represent and reason about systems a variety of metrics have been devised quantify their global characteristics. However, little is currently known how construct graph or improve an existing one given target objective. In this work, we formulate the construction as decision-making process in which central agent creates topologies by trial error receives rewards proportiona...

Let $H$ be a directed acyclic graph (dag) that is not rooted star. It known there are constants $c=c(H)$ and $C=C(H)$ such the following holds for $D_n$, complete on $n$ vertices. There set of at most $C\log n$ subgraphs $D_n$ covers every $H$-copy while $c\log does cover all $H$-copies. Here this dichotomy considerably strengthened.
 ${\vec G}(n,p)$ denote probability space graphs with ve...

‎An  oriented perfect path double cover (OPPDC) of a‎ ‎graph $G$ is a collection of directed paths in the symmetric‎ ‎orientation $G_s$ of‎ ‎$G$ such that‎ ‎each arc‎ ‎of $G_s$ lies in exactly one of the paths and each‎ ‎vertex of $G$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete‎ ‎Math‎. ‎276 (2004) 287-294) conjectured that ...

A compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. Directed Hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. Sets of extrema of Birkhoff polyhedra are mapped to tours ...

This work presents a new method for symmetrization of directed graphs that constructs an undirected graph with equivalent pairwise effective resistances as a given directed graph. Consequently a graph metric, square root of effective resistance, is preserved between the directed graph and its symmetrized version. It is shown that the preservation of this metric allows for interpretation of alge...