After the Game: Deeper Exploration Step 1: Recall Graph Coloring Basics Definition: In a graph, a proper vertex coloring assigns colors to each vertex such that no two adjacent (connected) vertices ...

PHP Graph Coloring Algorithm This PHP script demonstrates a graph coloring algorithm that assigns colors to vertices of a graph in a way that no adjacent vertices have the same color. It uses a ...

Graph colouring is a fundamental problem in both theoretical and applied combinatorics, with significant implications for computer science, operational research and network theory. At its essence ...

Sierpiftski graphs S (n,3) are the graphs of the Tower of Hanoi puzzle with n disks, while Sierpiftski gasket graphs Sn are the graphs naturally defined by the finite number of iterations that lead to ...

Theorem 3.5 For all we have Proof. (Figure 1) In graph, we have , because if we start coloring from the end point vertex u, this vertex at least is adjacent with j vertices. The vertex u with its ...

Article citations More>> Vitaver, L.M. (1962) Determination of Minimal Coloring of Vertices of a Graph by Means of Boolean Powers of the Incidence Matrix (Russian). Doklady Akademii Nauk SSSR, 147, ...

Based on the graph generation algorithm, we propose a novel algorithm to solve the problem of D(β)-vertices sum distinguishing edge coloring of some kinds of special graphs. Our main contributions to ...