Abstract: The b-chromatic number of a graph, written as φ(G), is the highest number of colors you can use to color the graph properly, with one special rule: in each color group, there must be at ...

Let G = (V(G), E(G)) be a graph. A set S ⊆ E(G) is an edge k-cut in G if the graph G − S = (V(G), E(G) \ S) has at least k connected components. The generalized k-edge connectivity of a graph G, ...

Antimagic labelling is a fascinating area of graph theory that assigns unique integers to the edges of a graph in such a way that the resulting vertex sums are distinct. This concept, grounded in the ...

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon. When you walk into a room full of people, you can ...

Power graphs provide an innovative way to visualise and analyse the algebraic structure of finite groups. In a power graph, the elements of a finite group serve as vertices, and an edge is drawn ...