Properties of the colour-distribution in edge-colourings of graphs are examined. The results are applied in generalizing two theorems of Vizing and in proving the following for m = 5 and 7: If G is ...

Let G be a directed graph such that every edge e of G is associated with a positive integer, called the index of e. Then G is called a network graph if, at every vertex v of G, the sum of the indices ...

Gene regulatory networks (GRNs) depict the regulatory mechanisms of genes within cellular systems as a network, offering vital insights for understanding cell processes and molecular interactions that ...