The Mathematics of Graphs  Lesson: Graphs and Euler Circuits In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. (Wikipedia) Terminologies under Graph https://courses.lumenlearning.com/wmopen-mathforliberalarts/chapter/introduction-euler-paths/ G E B I B C C A D F H A D Adjacent - two vertices are joined by an edge. Connected - a graph in which a path exists between any two vertices Components - connected parts of the graph Circuit - a path that starts and ends at the same vertex Degree of vertex - is the number of its neighbors Disconnected - not connected Edge - is unordered pair of vertices. Euler circuit - a path in a connected graph that starts and ends at the same vertex, and passes through every edge of the graph once and only once. Euler circuit - is a Euler path which starts and stops at the same vertex. Euler circuit - is a circuit that uses every edge in a graph with no repeats. Being a circuit, it must start and end at the same vertex. Euler path - a path in a connected graph that passes through every edge of the graph once and only once. Euler path in a graph or multigraph - is a walk through the graph which uses every edge exactly once. Euler path is a path that uses every edge in a graph with no repeats. Being a path, it does not have to return to the starting vertex. Graph - is a collection of vertices connected to each other through a set of edges. A graph G ...
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