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# D1 Definition

### D1 Definition based on Edexcel Markschemes

TermDefinition
Isomorphic graphs (same information but drawn differently)
connected graph Every pair of vertices connected by a path
Explain the term valency The valency of a vertex is the number of edges incident to it
tree Connected graph with no cycles
Define the term ‘matching’ A matching is a pairing of some or all of the elements of one set X, with elements of another set Y. Nodes in the same set cannot match to each other, e.g. X cannot match to X
Digraph edges of a graph have a direction associated with them
Spanning tree All nodes connected
Explain the difference between a complete matching and a maximal matching A maximal matching is where the number of edges is as large as possible without necessarily pairing all vertices. A complete matching pairs all vertices.
Minimum spanning tree A minimum spanning tree is a tree that contains all vertices and the total length of its arcs is as small as possible.
Write down, in terms of n, the number of arcs in the minimum spanning tree 𝑛 – 1
Define the term complete matching A matching where every member of set X is paired with a single member of set Y and vice-versa. Nodes in the same set cannot match to each other, e.g. X cannot match to X
Path a finite sequence of edges, such that the end vertex of one edge in the sequence is the start vertex of the next, and in which no vertex appears more than once.
Weighted graph (network) if a graph has a number associated with each edge
Cycle is a closed path. i.e. the end vertex of the last edge is the start vertex of the first edge
Simple graph is one in which there are no loops and not more than one edge connecting any pair of vertices
Define the term ‘alternating path’ A path from an unmatched vertex in one set to an unmatched vertex in the other set …which alternately uses arcs not in/in the matching
Created by: emaher5