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# D1 Definitions

### Graph Definitions

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