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 least one ...

Simon Špacapan, SEPARATION OF CARTESIAN PRODUCTS OF GRAPHS INTO SEVERAL CONNECTED COMPONENTS BY THE REMOVAL OF EDGES, Applicable Analysis and Discrete Mathematics, Vol. 15, No. 2 (October 2021), pp.

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.

Welcome to the Graph Theory course repository on GitHub! This repository is a central location for all the materials related to the course, including lecture notes, assignments, code samples, and ...

Abstract. Let 𝐼(𝐺;𝑥) denote the independence polynomial of a graph 𝐺. In this paper we study the unimodality properties of 𝐼(𝐺;𝑥) for some composite graphs 𝐺. Given two graphs 𝐺₁ and 𝐺₂, let ...

The study of such graphs is called graph theory. Engineers need to find planarity in a graph when, for example, they are designing a computer chip without a crossed wire.