The graph representation consists of 64 vertices corresponding to the squares of the board, with an edge between vertices if there is a legal knight move between the two squares.

This is a graduate-level introduction to graph theory, corresponding to a quarter-long course. It covers simple graphs, multigraphs as well as their directed analogues, and more restrictive classes such as …

A connected component (or just component) of a graph is a subset of the nodes such that: (1) every node in the subset has a path to every other node (2) the subset is not part of some larger set with …

Give an example of a graph for which you believe that this would be the case and provide a basic and intutive explanation of why you believe this would be the case.

Let us redraw our diagram of the city of KÄonigsberg by representing each of the land masses as a vertex and representing each bridge as an edge connecting the vertices corresponding to the land …

Can you draw the diagram below without taking your pen off the paper or going over the same line twice? In the diagram below, A,B,C,D are women and a,b,c,d are men. There is an edge joining x …

graph is a mathematical structure for representing relationships. A graph is a mathematical structure for representing relationships. Going forward, we're primarily going to focus on undirected graphs. The …