Graph Definitions
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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Graph | a set of vertices (or nodes) together with a set of edges
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Edge | a line with a vertex at each end
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Loop | an edge with the same vertex at each end
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Degree (or Order) of a Vertex | the number of edges incident on it
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Simple Graph | a graph where there are no loops, and in which there is no more than one edge connecting any pair of vertices
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Walk | a sequence of edges in which the end of one edge (except the last) is the beginning of the next
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Trail | a walk where no edge is repeated
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Path | a trail where no vertex is repeated
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Cycle | a closed path
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Hamiltonian Cycle | a cycle which visits every vertex
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When is a graph connected? | if a path exists between every pair of vertices
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Tree | a simple connected graph with no cycles
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Digraph (directed graph) | a graph is which at least one edge has a direction associated with it
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Complete graph | a simple graph in which every pair of vertices is connected by an edge
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Incidence Matrix | a way of representing a graph by a matrix
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Isomorphic Graphs | Two graphs are isomorphic if one can be stretched, twisted or otherwise distorted into each other
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Planar Graph | a graph which can be drawn without any edges crossing
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Bipartite Graph | a graph in which the vertices fall into two sets and in which each edge has a vertex from one set at one end and from the other set at its other end
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Created by:
Masterniket
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