Which of these are applications of graph isomorphisms? Verifying the layout of an electronic circuit produced by an automated tool. Determining the number of flights between each pair of cities in a transportation network. Determining whether an electronic circuit produced by a vendor uses intellectual property from a different vendor. Determining whether a chemical compound is the same as one already known. ☐ Determining whether a graph is bipartite.
A graph can exist in different forms having the same number of vertices, edges, and also the same edge connectivity. Such graphs are called isomorphic graphs.
Note that we label the graphs in this chapter mainly for the purpose of referring to them and recognizing them from one another.
Graph isomorphism is the area of pattern matching and widely used in various applications such as image processing, protein structure, computer and information system, chemical bond structure, Social Networks.
The Whitney graph isomorphism theorem, States that two connected graphs are isomorphic if and only if their line graphs are isomorphic, with a single exception: K3, the complete graph on three vertices, and the complete bipartite graph K1,3, which are not isomorphic but both have K3 as their line graph.
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