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IB HL discrete maths definitions
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Terms in this set (34)
weight
a number associated with an edge in a graph
cycle
a closed path
tree
a graph with no cycles
walk
any sequence of adjacent edges
circuit
a closed trail
edges
lines connecting vertices in a graph
degree
the number of edges coming out of a vertex
vertices
points in a graph
path
a walk with no repeated vertices
loop
an edge connecting a vertex to itself
trail
a walk with no repeated edges
connected graph
a graph in which it is possible to find a path from a vertex to any other vertex
bipartite graph
a graph whose vertices can be split into two groups such that only vertices from different groups are joined
multigraph
a graph where some edges are connected by more than one edge
complement of a graph
a graph consisting of all the edges that are not in the original graph
complete graph
a graph in which every pair of vertices is joined by an edge
simple graph
a graph with no loops or multiple edges between vertices
subgraph
a graph which is part of another graph
planar graph
a graph that can be drawn without edges intersecting
hamiltonian path
a path which includes every vertex of a graph
hamiltonian cycle
a closed path which includes every vertex
hamiltonian graph
a graph which contains a hamiltonian cycle
euler's relation
a rule relating the number of edges, vertices and number of regions of a planar graph
v-e+f=2
eulerian trail
a trail which uses each edge exactly once but does not return to the starting point
eulerian circuit
a closed trail around a graph which uses each edge exactly once. all vertices must be even
eulerian graph
a graph which contains a eulerian circuit. the graph can be drawn without taking the pen off the paper
semi eulerian graph
a graph that has a eulerian trail
relatively prime (coprime)
two integers whose gcd is 1
minimum spanning tree
the tree of smallest length that contains all the vertices of a graph
kruskal's algorithm
an algorithm for finding the minimum spanning tree
dijkstra's algorithm
an algorithm for finding the shortest path between two vertices in a graph
chinese postman problem
to find the route of shortest length which includes every edge of a graph and returns to the starting point
travelling salesman problem
to find the route of shortest length which includes every vertex of the graph and returns to the starting point
fundamental theorem of arithmetic
every positive integer greater than 1 can be expressed uniquely as a product of prime factors
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