Graph homomorphisms and chromatic numbers are foundational concepts in modern graph theory, with widespread applications that extend from combinatorial optimisation to theoretical computer science. A ...

Abstract The adjacent vertex-distinguishing total chromatic number of a graph 𝐺, denoted by χ𝑎𝑡(𝐺), is the smallest denoted by 𝑘 for which 𝐺 has a proper total 𝑘-coloring such that any two ...

Consider a finite nonnull graph $G$ with no loops or multiple edges and no isolated points. Its Ramsey number $r(G)$ is defined as the minimum number $p$ such that ...