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▾
Graph theory
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Matchings
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Minimum spanning tree
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Automorphisms of a graph
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Tournament graphs
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Basics of graph theory
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Intro to graphs
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Isomorphic graphs
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Walks, paths, and cycles
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Connected graphs
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Adjacency and degrees
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Subgraphs
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Graph components
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Adjacency lists, adjacency matrices, and incidence matrices
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Other simple planar graphs
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Regular graphs
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Intro to bipartite graphs
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Paths and cycles
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Eulerian cycles and paths
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Intro
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Using the theorem
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Hamiltonian cycles and paths
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Planar graphs
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Coloring
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Intro to vertex colorings
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Dijkstra's algorithm
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Fleury's algorithm
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Flows and cuts
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Kruskal's algorithm
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Minimum vertex covers
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Number of edges in a complete graph
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Perfect graph
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Size of tree is one less than order
▾
Trees
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Intro to trees
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Proving properties of trees
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Utilities puzzle
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What is a complete graph?
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What is a cubic graph?
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What is a maximal clique?
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What is an edge-induced subgraph?
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What is an irregular graph?
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What is a spanning subgraph?
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What is a vertex-induced subgraph?
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Intro to digraphs
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Combinatorics and graph theory
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Graceful labeling
›
Graph theory
›
Trees
Proving properties of trees
Let \(T\) be a graph. Then \(T\) is a tree if and only if there is exactly one path between any two vertices.
70219
Proof: Graph is a Tree iff Unique Paths for Each Vertex Pair | Graph Theory, Tree Graphs
Wrath of Math
7916
Path in Tree is Unique
ProofWiki