Terminology

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Graph – A visual representation of a set objects and relationships. Each member of X is represented as a vertex or node. Relationships are represented by edges or arcs.Vertex or Node – A point representing a member of the set.Edge or Arc – A link between vertices. An edge must have a vertex at each end.Loop – An edge with the same vertex at each end. Degree (order) of a vertex – The number of edges meeting at the vertex.Simple graph – Contains no loops and has no more than one edge between any pair of vertices.Walk – Sequence of edges. The end of each edge (except the last) is the start of the next.Trail – A walk with no repeated edges.Path – A trail in which no vertex is repeated.Cycle – A closed path. The end of the last edge joins the start of the first.Hamiltonian Cycle – A cycle that visits every vertex and returns to the start vertexHamiltonian Path – A path that visits every vertex.Connected – There is a path between every pair of vertices in a connected graph.Tree – Simple connected graph with no cycles.Digraph (directed graph) – Graph with at least one edge having a direction.Complete graph – A simple graph with each pair of vertices connected by an edge.Eulerian Graph – A graph in which every path can be traversed exactly once without lifting pen from paper. An Eulerian graph is connected and the degree of every vertex is even.Incidence Matrix – Matrix representation of a graph. Elements of the matrix show the number of edges connecting the vertices represented by the row and column of the matrix.Isomorphic – Graphs are isomorphic if one can be deformed to make the other. The vertices can be moved and the edges straightened or bent to do this.Planar graph – A graph that can be drawn such that no edges cross.Bipartite graph – A graph joining two sets of objects. Every edge starts in one set and ends in the other.

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