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-...

This paper explores which classes of graphs and matroids are k-balanced. A connection between k-balanced graphs and k-balanced matroids was also obtained. In this paper, we continue our study of the class of k-balanced matroids in order to see what matroid operations preserve k-balance. Since strong maps of matroids are defined as analogues of continuous maps of topological spaces, it is natura...

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...

In this note, we study the mixing properties of continuous-time quantum random walks on graphs. We prove that the only graphs in the family of balanced complete multipartite graphs that have a uniform mixing property are K2, K3, K4, and K2,2. This is unlike the classical case where the uniform mixing property is satisfied by all such graphs. Our proof exploits the circulant structure of these g...

In this paper, we establish a tight sufficient condition for the Hamiltonicity of graphs with large minimum degree in terms of the signless Laplacian spectral radius and characterize all extremal graphs. Moreover, we prove a similar result for balanced bipartite graphs. Additionally, we construct infinitely many graphs to show that results proved in this paper give new strength for one to deter...