If you are a coauthor you can get started by adding some content to it. Click the Insert or Insert Figure button below or drag and drop an image onto this text.

Graph theory is a topic used in discrete mathematics to show networks and study relationships between objects in a more mathematical way. Graphs consists of a a set of vertices usually denoted \(V,\) and an sets of edges typically denoted \(E.\) Each edge in a graph connects the vertices. A graph \(G\) is defined as an ordered pair where \(G=\left(V,E\right).\)

this is for holding javascript data

this is a placeholder for an editor

this is for holding javascript data

The vertices in the graph are \(V=\left\{1,2,3,4,5,6\right\}.\)

The edges in the graph are \(E=\left\{\left\{1,2\right\},\left\{1,5\right\},\left\{2,3\right\},\left\{2,5\right\},\left\{3,4\right\},\left\{4,5\right\},\left\{4,6\right\}\right\}\).

this is for holding javascript data

this is a placeholder for an editor

There are a few concepts within graph theory that include walks, paths, trails and cycles. A walk on a graph is defined as a sequence of adjacent vertices where repetition is allowed. A path is a walk, however, no vertices can be repeated in this case. Notice that within these two concepts, it is known that if a walk exists between \(x\) and \(y\), then a path also exists from \(x\) to \(y.\) Next, a trial is defined as a walk that has no repeated edges and a trail may be closed if it starts and ends with the same vertex. A cycle is a closed trail that does not have any repeated vertices besides their endpoints.

## Share on Social Media