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| Question | Answer |
|---|---|
| In Mathematics, this is a pictorial representation of any data in an organized manner. | Graph |
| It shows the relationship between variable quantities. | Graph |
| In a _____ _____, the graph represents the set of objects, that are related in some sense to each other. | Graph Theory |
| It is an ordered pair G = (V, E) consisting of a nonempty set V (called the vertices) and a set E (called the edges) of two-element subsets of V. | Graph |
| It is the study of relationship between the vertices (nodes) and edges (lines) | Graph Theory |
| It consists of a set of dots, called vertices, and a set of edges connecting pairs of vertices | Graph |
| Two types of graphs. | Directed and Undirected |
| It is a dot in the graph that could represent an intersection of streets, a land mass, or a general location, like “work” or “school”. Vertices are often connected by edges. | Vertex |
| It connect pairs of vertices. | Edges |
| It is a special type of edge that connects a vertex to itself. Loops are not used much in street network graphs. | Loop |
| It is the most general definition of how we can move around a graph. If we start at a vertex and then move along an edge to a new vertex, we are starting a walk. If we have a directed graph, we move in the direction of the arrows. | Walk |
| If a walk starts and ends at the same vertex then it is _____, and if it starts and ends at different vertices then it is _____. | closed, open |
| If a walk does not use the same edge more than once, then it is a _____. | Trail |
| Other term for closed trail | Circuit |
| It is a walk where no edge is repeated. | Trail |
| An ____ ____ starts and ends on different vertices | open trail |
| A _____ _____starts and ends on the same vertex. | closed trail (circuit) |
| All trails are? | Walks |
| All circuits are? | Closed walks |
| If a walk does not use the same vertex more than once (other than at the start and end) we call it a _____. | Path |
| When a path begins and ends at the same vertex it is a ____. | Closed path/cycle |
| A path is a walk where _____ | no vertex is repeated. |
| An open path starts and ends on _____ | different vertices. |
| • A closed path (cycle) starts and ends _____ | on the same vertex. |
| A closed trail can only use each edge once and must start and finish at ? | the same vertex |
| It is simply a rule associating vertices that preserves the edges joining the vertices. Consider the two graphs which are isomorphic under the correspondence: | An isomorphism |
| An _____ is a closed path that uses every edge in the graph exactly one. | Euler Circuit |
| A circuit that starts and ends at the same vertex. It also has an even degree of edges. | Euler Circuit |
| An ______ is a path that uses every edge in the graph exactly once but it does not start and end at the same vertex. | Euler Path |
| A path that also has an odd degree of edges. | Euler Path |
| A ______ is a path that visits each vertex exactly once. It was named after William Rowan Hamilton who studied them in the 1800's | Hamiltonian path |
| A ______ is a cycle which visits each vertex exactly once and also returns to the starting vertex. The graph that contains a Hamiltonian circuit is called Hamiltonian | Hamiltonian cycle |
| When a connected graph can be drawn without any edges crossing, it is called ____. | Planar |
| When a planar graph is drawn in this way, it divides the plane into regions called ____. | Faces |
| Euler's formula for planar's graph | v-e+f=2 |
Created by:
chok
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