Discrete Mathematics adjacency matrix incidence matrix subgraph graph
Discrete Mathematics adjacency matrix, incidence matrix, subgraph, graph operations, degree, handshaking theorem, graph isomorphism Liangfeng Zhang School of Information Science and Technology Shanghai. Tech University
Adjacency Matrix 0 1 0 1 0 0 0 1 0
Adjacency Matrix 2 1 0 1 0 1 1 0 0 1 0 2 0 1 1 2 0 1 0 0 0 1 0
Adjacency Matrix 0 1 1 1 2 1 0 0 1 0 2 1 0 1 0 1 2 0 0 1 0
Adjacency Matrix 0 1 0 0 0 0 1 0 REMARKS: The adjacency matrix is no longer symmetric
Adjacency Matrix 1 1 0 0 0 0 0 2 0 1 0 0 0 0 1 0
Incidence Matrix
Subgraph
Removing An Edge
Adding An Edge
Edge Contraction
Removing A Vertex
Complement
Degree 1 2 4 3 5 6
Degree 1 2 4 3 5 6
Handshaking Theorem
Handshaking Theorem 1 2 1 4 3 5 6 2 4 3 5 6
Graph Isomorphism
Graph Invariants DEFINITION: Graph invariants are properties preserved by graph isomorphism. For example, • The number of vertices • The number of edges • The number of vertices of each degree REAMRKS: The graph invariants can be used to determine if two graphs are isomorphic or not. There is no vertex of degree 4 in the 1 st graph Induced subgraphs are not isomorphic. Original graphs are not isomorphic. The subgraphs induced by the vertices of degree 3 must be isomorphic to each other.
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