A locally irregular graph is a in which the end vertices of every edge have distinct degrees. coloring G any such that each colors induces subgraph G. colorable if it allows coloring. The chromatic index G, denoted by χirr′(G), smallest number used local irregularity conjecture claims all graphs, except odd-length paths, cycles and certain class cacti are three colors. As valid for graphs with ...

A rigorous understanding of brain dynamics and function requires a conceptual bridge between multiple levels of organization, including neural spiking and network-level population activity. Mounting evidence suggests that neural networks of cerebral cortex operate at a critical regime, which is defined as a transition point between two phases of short lasting and chaotic activity. However, desp...