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Graph Theory (Graph terminology (A walk is a sequence of edges., A tail is…
Graph Theory
Graph terminology
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A path is a walk with distinct vertices. In a path, each edges can be travelled only once.
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A graph is connected if there is a path from any one of its vertices to any other vertex. If this is not possible then the graph is disconnected. A disconnected graph is made up of components.
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The distance between vertices u and v in G, written as d(u, v) is the length of the shortest path between u and v.
The diameter of graph G, written as diam(G) is the maximum distance between any two points in G.
Formal Definition
V is a set of vertices, nodes or points.
Vertex set of G is usually denoted by V(G), or V.
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Graph terminology
Digraphs: A digraph is a directed graph where the edges connecting the vertices have directions associated with them.
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Isomorphic graphs: Graphs are isomorphic if they can be drawn in many ways, but provide the same information.
A subgraph: a subgraph of G is a graph H, where V(H) ⊆ V(G) and E(H) ⊆E(G).
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