• TOC
  • Courses
  • Blog
  • Twitch
  • Shop
  • Search
    • Courses
    • Blog
    • Subreddit
    • Discord
    • Log in
    • Sign up
    • ▾Graph theory
      • •Matchings
      • •Minimum spanning tree
      • •Automorphisms of a graph
      • •Tournament graphs
      • ▾Basics of graph theory
        • •Intro to graphs
        • •Isomorphic graphs
        • •Walks, paths, and cycles
        • •Connected graphs
        • •Adjacency and degrees
        • •Subgraphs
        • •Graph components
        • •Adjacency lists, adjacency matrices, and incidence matrices
        • •Other simple planar graphs
        • •Regular graphs
      • •Intro to bipartite graphs
      • ▸Paths and cycles
        • ▸Eulerian cycles and paths
          • •Intro
          • •Using the theorem
        • •Hamiltonian cycles and paths
      • •Planar graphs
      • ▸Coloring
        • •Intro to vertex colorings
      • •Dijkstra's algorithm
      • •Fleury's algorithm
      • •Flows and cuts
      • •Kruskal's algorithm
      • •Minimum vertex covers
      • •Number of edges in a complete graph
      • •Perfect graph
      • •Size of tree is one less than order
      • ▸Trees
        • •Intro to trees
        • •Proving properties of trees
      • •Utilities puzzle
      • •What is a complete graph?
      • •What is a cubic graph?
      • •What is a maximal clique?
      • •What is an edge-induced subgraph?
      • •What is an irregular graph?
      • •What is a spanning subgraph?
      • •What is a vertex-induced subgraph?
      • •Intro to digraphs
      • •Combinatorics and graph theory
      • •Graceful labeling
     › Graph theory › Basics of graph theory

    Adjacency and degrees

    Students will learn what it means for vertices to adjacent, as seen here. They'll also learn how to determine the degree of a vertex, as seen here. Then they'll learn what the Handshaking lemma says and how to prove it. Further, students will learn how the Handshaking lemma can be used to prove that every graph has an even number of odd degree vertices. Here's a video on the Handshaking lemma and its corollary.

    Lessons and practice problems