Optimization and reduction of costs in management of distribution and transportation of commodity are one of the main goals of many organizations. Using suitable models in supply chain in order to increase efficiency and appropriate location for support centers in logistical networks is highly important for planners and managers. Graph modeling can be used to analyze these problems and many oth...

We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we introduce a graph, called a reaction graph, that has one edge for each reaction but potentially multiple nodes for each complex. A special class of steady state...

We call a simple graph highly irregular if each of its vertices is adjacent only to vertices with distinct degrees. In this paper we examine the degree sequences of highly irregular graphs. We give necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a highly irregular graph.

Nash-Williams’ well-balanced orientation theorem [11] is extended for orienting several graphs simultaneously. We prove that if G1, ..., Gk are pairwise edge-disjoint subgraphs of a graph G, then G has a well-balanced orientation ~ G such that the inherited orientations ~ Gi of Gi are well-balanced for all 1 ≤ i ≤ k. We also have new results about simultaneous well-balanced orientations of non-...

1 CONTENTS 2 Figure 1: A partitioned 2D irregular mesh of an airfoil. The shading of a mesh element indicates the processor to which it is mapped. 0.1 Introduction Algorithms that nd good partitionings of unstructured and irregular graphs are critical for the eecient execution of scientiic simulations on high performance parallel computers. In these simulations, computation is performed iterati...

1 CONTENTS 2 Figure 1: A partitioned 2D irregular mesh of an airfoil. The shading of a mesh element indicates the processor to which it is mapped. 0.1 Introduction Algorithms that nd good partitionings of unstructured and irregular graphs are critical for the eecient execution of scientiic simulations on high performance parallel computers. In these simulations, computation is performed iterati...

A graph is balanced if its clique-vertex incidence matrix is balanced, i.e., it does not contain a square submatrix of odd order with exactly two ones per row and per column. Interval graphs, obtained as intersection graphs of intervals of a line, are well-known examples of balanced graphs. A circular-arc graph is the intersection graph of a family of arcs on a circle. Circular-arc graphs gener...

A colouring of a strongly regular graph is an allocation of colours (or treatments) to the vertices of the graph. Such a colouring is balanced if every pair of distinct colours occurs equally often on the ends of an edge. When the graph is the complete regular multipartite graph a balanced colouring is just a balanced incomplete-block design, or 2-design. Some constructions are given. For examp...

We introduce and study the Doubly Balanced Connected graph Partitioning (DBCP) problem: Let G=(V,E) be a connected graph with a weight (supply/demand) function p:V→ {−1,+1} satisfying p(V )= ∑ j∈V p(j)=0. The objective is to partition G into (V1, V2) such that G[V1] and G[V2] are connected, |p(V1)|, |p(V2)|≤cp, and max{ |V1| |V2| , |V2| |V1|}≤cs, for some constants cp and cs. When G is 2-connec...